Tangent line Definition and 278 Threads

Homework Statement find the slope of the tangent line whose g(x)=x^2-4 at point (1,-3) Homework Equations lim f(x+Δχ) -F(c)/ (Δχ) The Attempt at a Solution g(x)= x^2-4 G(1+Δχ)= (1+Δχ)^2-4 ==> Δχ^2+2Δχ-3 lim (Δχ^2+2Δχ-3) - (-3)/(Δχ) = 0 but in the book the answer is 2 so what...

Homework Statement I seem to remember that a parameterized a(t) curve in \mathbb{R}^3 that one can construct the tangent from the slope of a'(t) and the curve itself. such that the tangent line L = a(t) + s * a'(t) to a. This is supposedly a straight line in \mathbb{R}^3. To make a...

Homework Statement If the tangent line to y = f (x) at (9,7) passes through the point (0,6), find the following. (a) f (9) (b) f ' (9) Homework Equations f '(x) = f(x+h) - f(x)/h ? The Attempt at a Solution I really have no idea how to even begin going about this one, so a...

I am having a time trying to figure out this problem given only an x value. The equation is "Find the equation of the tangent line to y= Square root of x^4-2337 ...at x=7. If anybody could help me solve this it would be a great help. Thanks

An Unknown Conic and Equation of Tangent Line **HELP** Homework Statement (a) Find the positive y-coordinate of the point on the conic whose x-coordinate is 27cos\theta, where 0<\theta<\pi/2 (b) The slope of the tangent line to the conic through the point (27cos\theta, y1) is -1/27cot\theta...

The curve defined by x3 +xy - y2 = 10 has a vertical tangent line when x = ? To find when the tangent line is vertical, could I find when the slope is undefined for the original function? The way I previously tried this problem was by taking the first derivative and then finding when x = 0...

Homework Statement Find the equation of the tangent line to the curve 3xy = x^3 + y^3 at point (2/3,4/3) Homework Equations The Attempt at a Solution I found the deriviative to be 3x^2-3y / 3x - 3y^2 which i simplified to x^2 - y / x - y^2 I found the slope of at those...

Homework Statement Let C be the intersection of the two surfaces: S1: x^2 + 4y^2 + z^2 = 6; s2: z = x^2 + 2y; Show that the point (1, -1, -1) is on the curve C and find the tangent line to the curve C at the point (1, -1, -1). Homework Equations partial derivates, maybe the gradient...

Homework Statement Find an equation for the line tangent to to the graph of f^-1 at the pt (3,1) if f(x)=x^3+2x^2-x+1 Homework Equations The Attempt at a Solution I used the Inverse Function Thm 1/(3x^2+4x) Now do I plug in 3 to this to find slope? 1/21 y-1=1/21(x-3)...

Homework Statement Find parametric equations of the tangent line at the point (-2,2,4) to the curve of intersection of the surface z=2x2-y2 and the plane z=4 Homework Equations Not sure The Attempt at a Solution Not sure quite how to approach this. take the gradient of...

Homework Statement Find an Equation of the tangent line to the curve y=10^x at the point (1,10) Homework Equations Derivative y=mx+b The Attempt at a Solution I am totally lost I don't know what to do with 10^x Please help me this will save me failing the class

Homework Statement On the circles y^2+x^2=1 and y^2+(x-3)^2=4 There is a line with positive slope that is tangent to both circles. Determine the points at which this tangent touches each circle. Homework Equations the derivative of the first circle i found: y'=-x/y the derivative of...

Homework Statement The tangent line through given points (pi/4,pi/4) m=1 y= cos(y)cos(x)/sin(x)sin(y) The Attempt at a Solution dy/dx= d/dx[cos(y)cos(x)/sin(x)sin(y)] First use quotient rule ? vu'-uv'/v^2 v= sin(x)sin(y) v'= do i need to use product rule? for product rule...

Homework Statement Find the slope of the tangent line to the curve y=x3 at point (-1,-1) (i) Using Definition 1 m=limx-->a\frac{f(x)-f(a)}{x-a} (i) Using Equation 2 m=limh-->0\frac{f(a+h)-f(a)}{h} Homework Equations The Attempt at a Solution For the first one, I got as far...

Homework Statement Ok, how do i solve this question I've attached the picture.. The answer is A but i don't understand how to get that... The Attempt at a Solution The solution is also given , but i don't understand the adding and subtracting 5. the Derivative of y=ln (e^x + 5) y'=...

Find the slope of the functions graph at the given point. F(x) = x / x-2 point (3,3) f(x+h) - f(x) / h is what we have to use to find the answer. so I've plugged it all in and have came to this.. ((3+h) / (3+h-2)) - 3 / h I need some help with my simplification...

Find an equation for the line tangent to the given path at the indicated value for the parameter. x(t)=4costi-3sintj+5tk, t=\pi/3 So what I did here was take x'(t) and then plugged in \pi/3 after that to get an equation containing i, j, and k. x'(t)= -4sinti-3costj+5k...

Homework Statement Find the unit vectors that are parallel to the tangent line to the curve y=2sinx at the point (\pi/6, 1). Thereafter, find the unit vectors that are perpendicular to the tangent line. Homework Equations The Attempt at a Solution I took the derivative of y=2sinx and...

Let f be the funtion given by f(x) = 4x^2 - x^3 , let L be the line y = 18 - 3x, where L is tangent to the graph of f. Show that L is the tangent to the graph of y= f(x) at the point x = 3. I'm equaling both graphs like this: 4x^2 - x^3 = 18 - 3x and then I isolate everything...

A tangent to a curve is a line that touches the curve but at what specific point where there is a slope to the curve. Equations like y = X^2 have many slopes because the curve is shaped differently at different points. We can choose 2 points on the graph and find the slope but it will...

Homework Statement Find an equation of the tangent line to the curve y = 5x3 at the point (-3,-135). Enter your equation in y = form. Homework Equations The Attempt at a Solution Taking the derivative of the equation I get y = 15x2, following that I plug in the x value of...

Homework Statement Find the equation of the tangent line to the graph of x^2 - xy + y^2 = 19 (where y=y(x)) at (3,-2). Homework Equations The Attempt at a Solution So, this is what I did: d/dx(x^2-xy+y^2) = (19)d/dx 2x*dx/dx-dy/dx+dy/dx+2y(dy/dx)=0 2x+2y(dy/dx)=0 And I...

Homework Statement Find equation of the tangent line at t=0 x=2sint y=tant The Attempt at a Solution Really don't know where to start, can someone give me the hint, don't solve it, i want to try it, just need a hint

Homework Statement Find the smallest positive value for `theta` for which the tangent line to the curve `r = 6 e^(0.4 theta)` is horizontal The Attempt at a Solution I tried to use the (r'sin(theta)+rcos(theta))/(r'cos(theta) - rsin(theta)) formula to get the tangent line, which I got...

Homework Statement Find all points on the graph of the function at which the tangent line is horizontal. f(x) = 2sinx + (sinx)^2 Homework Equations Hi guys I have an issue. I do not know how to approach this problem. I know the chain rule but I still do not know how to solve the...

Homework Statement The equation of tangent is given t:2x+3y-2=0 and the equation of elipse E:x^2+4y^2=K Find "a" and "b" and the coordinates of touching point D. Homework Equations equation of elipse: b^2x^2+a^2y^2=a^2b^2 equation for touching: a^2k^2+b^2=n^2 equation for K (if...

For which value of x...horizontal Tangent Line Homework Statement For which value of x does f(x) = \frac{k}{ax^{2}+bx+c} have a horizontal tangent line? Homework Equations Quotient Rule? F'(x) = [g(x)a'(x) - a(x)g'(x)]/g(x)^2? The Attempt at a Solution Am I supposed to...

Homework Statement At which point is the tanget line to the following curve horizontal? y= a sin^{3}\theta x = acos^{3}\theta Homework Equations The Attempt at a Solution \frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} When \frac{dy}{dx} = 0 , this means that that the tanget...

I have encountered a problem in my Calculus homework. I have a position function, r(t)= (t^2)i + (4t)j and in my homework, I am asked to find the tangent to this curve at the point t=3. I did this by finding dy/dx, or 2t/4 @ t=3 is 6/4. However, I am also asked to relate this to the...

Given equation x^2/9 + y^2/4 = 1. Determine the two points on the ellipse having a tangent line passing through the point (0,3). Cant seem to figure this one out? I have found the derivative of the slope which is -4x/9y. I don't know how to use that slope in order to find a tangent line that...

1. Find the equations of all tangents to the graph f(x) = x^2-4x + 25 that pass through the origin. 2. The relevant equations to my knowledge are the slope formula and f ' (x) 3. First I found the derivative using various rules to be f ' (x) = 2x - 4 after this i used the slope formula and my...

Hello, I'm having trouble understanding an example from my test and I would appreciate your help clarifying how to get from one step to the next. Problem: Find an equation of the tangent line to the hyberola y = 3/x at the point (3,1) Eqation: m = \frac{f(a+h) - f(a)}{h} m =...

Hi, I'm having trouble plotting the tangent line on a curve (or the derivative evaluated at a point) in spice. I know how to plot the derivative of the entire curve using the d() function, but I don't know how to evaluate it at a point. Any help is much appreciated!

Sorry if the title is a bit vague :/ The Problem: Find the point on the parabola y=1-x^2 at which the tangent line cuts from the first quadrant a triangle with the smallest area. Relevant Equations: y = 1-x^2 ; y' = -2x ; A= 1/2bh I'm basically stuck near square one, I found...

1. The problem statement, all variables and given/known i have to find all tangent lines in the equation below that pass though the point (0,0) y=x^{3}+ 6x^{2}+8i took the derivative and got this. y=3x^{2}+12x then i substituted the points x=0 and y=0 into the derivative equation and the...

Homework Statement if the tangent line to the graph of y=f(x) at (2.3) has an equation x-y+1=0, then f'(2) =? The Attempt at a Solution We did these problems in one small session at the beginning of the semester, but my notes aren't clear and I am not sure where to begin. Do I just...

i would like to know if my answer is correct can someone tell me the results for this: Find the equation of the tangent line to x^3-2x^2y+y^2=17 at (2,-1) ive gotten y'=(3x^2+4xy)/(-2x^2-y) and my line equations is y+1=(-1/4)(x-2) thanks in advance

Homework Statement Find the tangent line to the curve y^2 (y^2 - 4) = x^2 (x^2 -5) at the point (0,-2). Homework Equations y-y1=m(x-x1) The Attempt at a Solution I d/dx-ed both sides and was left with dy/dx=0 so y=-2 Does that seem right?

[SOLVED] Derivative and tangent line Homework Statement y = (x)/(x+x^-1) Find an equation of the tanget line to the graph at x=2 Homework Equations The Attempt at a Solution I used the quotient rule and got the derivative to be 0 / (x+x^-1) = y' so then the slope is 0 of the...

[SOLVED] Tangent Line Homework Statement Find all tangent lines that are tangent to Y=x^2 and go through the point (2,3) Homework Equations The Attempt at a Solution At first I thought I knew how to do this problem, I found the derivative of the equation got: y' = 2x ; then...

Homework Statement Find parametric equations for the tangent line to the curve x= t^4, y= t^4, z=t^3 at the point (1,1,1) Homework Equations The Attempt at a Solution I understand everything about solving this problem with the exception of how to find what t =? to plug in. ie...

Homework Statement suppose y=2x-3 is an en equation of the tangent line to the graph of y=f(x) at the point where x=2. find the value of f'(2) and f(2). Homework Equations I know how to get the tangent line, but this wording throws me off. a little help at how to solve f(2) and f'(2)...

Homework Statement Find an equation of the tangent line to the curve: 7*x*e^(x)+8 at (0,8) Homework Equations Derivative I guess? The Attempt at a Solution I know you have to take the derivative of the equation given which I think is 7*x*e^(x) + 7*e^(x) Then you plug it...

Homework Statement find the equation for the tangent line. 1. (e^x)(cos x) where x=0Homework Equations plugged 0 into the equation, (e^0)(cos 0) and got 1 for the y-coordinate. so I got the points(0,1). For the slope, I derived the equation into -(e^x)(sin x). then i plugged 0 in and got 0 for...

Homework Statement 5. Find parametric equations for the tangent line to the curve of intersection of the surfaces z^2 = x^2 + y^2 and x^2 + 2y^2 + z^2 = 66 at the point (3, 4, 5). The Attempt at a Solution f(x,y,z) = x^2 + y^2 - z^2 g(x,y,z) = x^2 + 2y^2 + z^2 Partial derivz...

What is the difference between a normal line and a tangent line?

Homework Statement Find the equation of the tangent line to the curve at the given point. y = \sqrt{2x+1} , (4, 3)Homework Equations a = 4 M =\lim_{x \to a} \frac{f(x) - f(a)}{x-a} or Mpq = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} The Attempt at a Solution M =\lim_{x \to 4} \frac{f(x) -...

y=1+2x-xcubed, (1,2)

Hi, I was wondering if anyone could help. Consider the curve given by: 2y^3 + (6x^2)y - 12x^2 + 6y = 1 I solved the derivative which came out to be (4x-2xy)/(x^2 + y^2 + 1 1. Write an equation of each horizontal tangent line to the curve. 2. The line through the origin with slope -1...

Hi, I am having problems with the following problem. The main issue is actually starting the problem. Find the two points on the curve y = x^4 - 2x^2 - x that have a common tangent line.