Tangent line Definition and 278 Threads

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Homework Statement Q: Does the graph of f(x) = x^(1/2) have a point of tangency with the line y = (x/4) + 1? Homework Equations lim x->a (f(x) - f(a)) / (x-a) The Attempt at a Solution If the limit exists of the relevant equation than there is a point of tangency. So I'm...

I need to find the tangent line to the curve xe^Y+ye^x=1 at the point (0,1). I took the derivative and found to be: dy/dx=-(ye^x-e^y)/(xe^y+ye^x) I set that equal to 0 so: 0=-ye^x-e^y I have tried using a natural log to get y on one side and x on the other, but so far no good. How can...

Homework Statement Find the pt. at which the tangent line to the curve x=3t^2 - t, y=2t+t^3 at t=1 intersects the line y=2-x. Homework Equations Possibly <6t-1, 2+3t^2> if the tangent is not already present The Attempt at a Solution I am confused about how to go about solving...

https://www.physicsforums.com/attachments/2227 The region $R$, is bounded by the graphs of $$ f(x)=x^2 -3$$ and $$g(x)=(x-3)^2$$, and the line $$T$$, as is shown in the figure above. $$T$$ is tangent to the graph of f at point $$(a,a^2-3) $$ and tangent to the graph of g at point...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Hey y'all, this is my first post. I am currently stuck on a multivariable question. Please let me know if you can help. Homework Statement The point, P = (1, 2, 2) lies on the surface z = x^2 + y^2 -3x. Find parametric equations for the tangent line to the surface through the point P parallel...

Homework Statement I was given parametric equations. x(t) = a(t) y(t) = b(t) z(t) = c(t) where a, b, and c are functions that depend on t. I was supposed to find equation of the tangent line at t = f given: x(f)= m y(f) = n z (f) = o where m,n,o are some constant numbers...

Find the slope of the tangent line to the curve f(x)=x-x^3 at the point (1,0) So, I went through and plugged (a+h) in everywhere I saw "x" (a+h)-(a+h)^3 Factoring: (a+h-a^3-3a^2h-3ah^2-h^3) I'm really stuck on what to do next...I don't see anything you can cancel/pull out? I know...

Hello All, I have been trying to brush up on some calculus (differential, I haven't learned integral yet) on my own by finding whatever calculus problems I can find. Recently I found this question listed as a CLEP practice question, and have been having some difficulty with it. Here is the...

Given the parametric equations, find an equation of the tangent line at the given point on the curve. Homework Statement Find an equation of the tangent line at each given point on the curve: x = 2cotΘ and y=2sin^{2}θ at point (\frac{-2}{\sqrt{3}},\frac{3}{2}) Homework...

find the equation of the tangent line.$$y = e^{3x + cos x}$$ @ x = 0 $$ y1 = e^{3(0) + cos(0)} = e^1 = e$$ $$y1 = e$$ $$y = e^{3x+cos x}$$ $$y' = e^{3x + cos x} * (3 - sinx)$$ $$m = 3e$$ $$ y - e = 3e(x - 0) $$

Find the equation of the tangent line to g(x) = arctan(x) + ln(x) @ x = 1 $$y - \frac{\pi}{4} = \frac{3}{2}(x - 1)$$

This is my first post, and I'm excited to be able to receive quality help from what seems to be a good place. I'll attempt to start using the proper format and make it easy for everyone to read, thank you for the help! This should be a simple problem, but I seem to have forgotten how to do it...

1. If an equation of the tangent line to the curve y=f(x) at the point a=2 where is y=4x-5, find f(2) and f'(2). Homework Equations [SIZE="4"]m=\frac{f(x)-f(a)}{x-a} The Attempt at a Solution To be honest, I really don't know where to start. Here's what I have so far...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Here is the question: I have posted a link there to this topic so the OP can see my work.

The line y = ax + b is tangent to y=x3 at the point P = (-3,-27). Find a and b. I'm pretty lost on this one. Here's my initial thoughts. Find (a) first. (a) is equal to the slope which is the derivative of x3 So (a) would be equal to 3(-3)2 ? Not quite sure where to start on this one.

Homework Statement I don't know how to make theta so ∅ = theta. find the slope of the tangent line at r = sin(6∅) when ∅ = pi/12 Homework Equations y=rsin(6∅) x=rcos(6∅) r=sin(6∅) tangent line equation y-y' = m(x-x') m = dy/dx The Attempt at a Solution when ∅ = pi/12 then...

Homework Statement Find an equation of the tangent to the curve given by x=tan(∅) y=sec(∅) at the point (1,sqrt(2)) The answer should be in the form y=f(x) without ∅ The Attempt at a Solution Tangent line equation... y-y*=m(x-x*) m = dy/dx m = sec(∅)tan(∅) / (sec^2(∅) m = tan∅...

I don't need an answer, I'm just stumped as to how to properly turn these into point slope form to find the tangent, can anyone guide me through this? Help would be greatly appreciated. I believe I understand the formulas that are used to solve problems such as these. It starts by finding the...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

Homework Statement Find the equation of the tangent line at the curve y= x * e^(2x) at the point (2, 2*e^(4)) Homework Equations The Attempt at a Solution f'(x)= e^(2x) * (2x+ 1) (e^4)(5) = 5e^4 y- 2*e^4 = 5*e^4 (x-2) y= 5(e^4)*x - 8*(e^4) Is this right? It seems too easy...

Homework Statement Find the points on the graph of x3-y3=3xy-3 where the tangent line is horizontal Homework Equations y = f(x) so implicit differentiation must be used when taking the derivative of y (xy)' = xy' + y The Attempt at a Solution So if the tangent line is...

Homework Statement Determine a line that is tangent to both f(x)=x2 and g(x)=x2-2x Homework Equations The Attempt at a Solution f(x)=x2 => f'(x)=2x g(x)=x2-2x => g'(x)=2x-2 f'(a) = f'(b) 2a = 2b-2 I don't know how to continue. Thanks for help.

Homework Statement Give the equation of the line tangent to the curve at the given point. ytan^-1x = xy at (sqrt3,0) Homework Equations The Attempt at a Solution Would it be right to do an implicit differentiation or to isolate for y here? I isolated for y and got...

Homework Statement Find an equation of the tangent line at the point indicated f(x) = 5x2-2x+9 , x = 1 Homework Equations (d/dx) bx = ln(b)bx General Power Rule which states: (d/dx) g(x)n = n(g(x))n-1 * g'(x) The Attempt at a Solution So looking at a previous problem...

Here is the question: Here is a link to the question: Finding tangent line with definite integral? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Given that the curve y = x^3 has a tangent line that passes through point (0, 2), find the area of the region enclosed by the curve and the line by the following steps. Homework Equations The Attempt at a Solution Let f(x) = x^3 and let the coordinates of the...

Homework Statement If f(x,y) = xy, find the gradient vector \nabla f(3,2) and use it to find the tangent line to the level curve f(x,y) = 6 at the point (3,2) Homework Equations The Attempt at a Solution f(x,y)=xy \Rightarrow\nabla f(x,y)=<y,x>,\nabla f(3,2)=<2,3> \nabla...

1. Given. F(x) = 4x/(x^2+1) 2. Problem Find all points (x,y) where the function has a horiztonal tangent line 3. Attempt I took the derivative of F(x) and came to (-4x^2+4)/(x^2+1)^2 I set it equal to zero and found an x value of 1. I used that x value and plugged it into...

Homework Statement At what points on the curve y = (x^2)/(2x+5) is the tangent line horizontal? Homework Equations Quotient rule The Attempt at a Solution I figured out the derivative which is 2x(2x+5) - 2x^2 ----------------- (2x+5)^2 I also know that for the equation of...

Here is the question: Here is a link to the question: An equation of the tangent line to the curve y=f(x)=x(10cos x- 2sinx) at the point (4pi, f(4pi)) is y=? - Yahoo! Answers I have posted a link there to this topic, so the OP can find my response.

"find a unit tangent vector and the equation of the tangent line to the curve r(t) = (t, t^2, cost), t>=0 at the point r(pi/2)." NOW, what I don't get is, how is that a curve? This is not like the example I have studied and I don't really get the question. So I don't know where to start. Once I...

Homework Statement Find the number of tangent lines to the curve: y=\frac{3x}{x-2} which pass through the point (-1,9). Find also the points of contact of these tangent lines with the curve.The Attempt at a Solution 1. I found the equation of lines passing through (-1,9) -> y=(x+1)m+9 2. I...

1. Find the values for x at which the tangent line is horizontal 2. f(x) = x + 2sinx 3. I found the derivative to be f'(x) = 1 + 2cosx I then set the derivative equal to zero and it came out to be 2cosx = -1, cosx = -\frac{1}{2} So the values of the horizontal tangent are 2∏/3 ± 2∏

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Homework Equations x = t \\ y = e^{-4t} \\ z = 5t - t^5 \\ P = (0, 1, 0) The Attempt at a Solution \vec{r}(t) = < t, e^{-4t}, 5t - t^5 > At the point...

Homework Statement Find the equation of y^2=x(x-3)^2 of tangent line at (3,0) Homework Equations Given above. I think implicit differentiation is involved or no since there is no xy's on the same side? The Attempt at a Solution Anyways... My attempt: 2ydy/dx = x*2(x-3)*1...

Homework Statement I've got the equation of a parabola y=2x^2-4x+1 with point (-1,7) and a tangent line running through it the point. I'm supposed to find the equation of the line. Simultaneously solve this equation with that of the parabola, place the results in form ax^2+bx+c, and find the...

1.Find the y-intercept of the tangent line to: y= -.4/√(3 + x) at [2.5, -.170560573084488] 2. So I thought the first step would be to find the slope of the tangent line. I think we find the slope of the tangent line by taking the derivative. So I am going to use the Quotient Rule to take...

Find the equation of the line tangent to f(x)= 3x^3 + 2 at x = 1. a) y = 9x-4 b) y = 9x+5 c) y = 3x 2 d) y = 3x+1 e) Not enough information given. Im confused on this one, but I am thinking about E, because it doesn't specify if the equation should be parallel or perpendicular to the...

I am asking for simple guidance on this problem. f(x) = 3x^2-1, (2,11)I do believe I need to obtain an equation for tan line so first step I think is to use point slope or slope intercept (a friendly reminder to the name of formula would be very nice :)) y - ysub1 = m(x-xsub1) = y -...

Homework Statement The equations ##2x^3y+yx^2+t^2=0##, ##x+6+t-1=0## implicitly define a curve $$f(t) = \begin{pmatrix} x(t)\\y(t) \end{pmatrix}$$ that satisfies ##f(1)=\begin{pmatrix} -1\\1 \end{pmatrix}.## Find the tangent line to the curve when ##t=1##. Homework Equations The...

Homework Statement Find the equation of the tangent line of tan(xy2)=(2xy)/\pi at (-\pi,1/2) Homework Equations The Attempt at a Solution I managed to get the equation into its dy/dx form and for the slope to be (1-.5pi)/(2pi-2pi2) This seems far to complicated to be correct though.. can...

Homework Statement Find the points on the graph y=x^3/2 - x^1/2 at which the tangent line is parallel to y-x=3. Homework Equations The Attempt at a Solution First I found that the derivative of y=x^3/2 - x^1/2 is 1x. I then rewrote the other line as y = 3+x and found the...

Homework Statement \frac{3x+6}{2-x} at x=3 Homework Equations y - y_{o} = m(x-x_{o}) The Attempt at a Solution f(3) = -\frac{15}{4} m = \frac{3}{0} DNE I have to write the equation in the form of the point-slope formula. I can get x_{o} and y_{o}, but I am...

Homework Statement Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P r(t)= <2sin(t), 2cos(t), 4sin2(t)>, P(1, √3, 1) The Attempt at a Solution I found T(t) using the formula T(t)= r'(t)/||r'(t)|| r'(t)= <2cos(t)...

Homework Statement Hello again. The question asks me to find an equation of the tangent to the graph: f(x)= - sin^2 x + 1/2, ~x~\epsilon~[0, \frac{\pi}{2}] which makes an angle of 135° with the x-axis (measure anti-clockwise from the positive x-axis). Assume that the scales along...

Homework Statement Hello again. The question asks me to find an equation of the tangent to the graph: f(x)= - sin^2 x + 1/2, x \epsilon [0, \frac{\pi}{2} which makes an angle of 135° with the x-axis (measure anti-clockwise from the positive x-axis). Assume that the scales along the...

Homework Statement This problem is 2.95 of University Physics, 11th edition. Catching the Bus: A student is running at her top speed of 5.0 m/s to catch a bus, which is stopped at the bus stop. When the student is still 40.0 m from the bus, it starts to pull away, moving with a constant...