Tangent line Definition and 278 Threads

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at a given point. \[x = t^5, y = t^4, z = t^3\] at point (1,1,1) Homework Equations The Attempt at a Solution So we need to have direction vector, and a point. To find...

Homework Statement So, it's my understanding that there must exist a line which is tangent to a given circle and intersects a given point in 2D space. I'm trying to find that line. Any form will do, but I'm currently aiming for the coordinates of the two points: the intersection point, and the...

Homework Statement Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point. (x - y - 1)3 = x; (1, -1) The Attempt at a Solution x3-y3=1 3y2(dy/dx)-3x2=0 3y2(dy/dx)=3x22 (dy/dx)=3y2/3x2 (dy/dx)=x2/y2 slope = (dy/dx) = 1...

Find the x-coordinate of all points on the curve y = sin(2x) + 2 sin(x) at which the tangent line is horizontal. Consider the domain x = [0,2π). f'(x)=2cos2x+2cosx

Homework Statement Find the parametric form for the tangent line to the graph of y=2x2−5x+3 at x=2 is Homework Equations I have no clue! The Attempt at a Solution I found the tangent line to be y=3x-5 I know that the answer has to be in the form... <x0,y0>+t<x1-x0,y1-y0> I...

If the first derivative of a function represents the gradient of the tangent line... What does the second derivative represent? Thanks in advance James

Say I have a curve is called C: y=1287*x^-1.5 Find a tangent line to the C, and the tangent line has to have a intercept of 150. This is not a homework, not at all.

Finding the Equation of Tangent line on cos wave! Find the equation of the normal line to y = 2cos ( 4x) at x = \pi / 3 I don't even know where to start with this question, i have searched the textbook and internet, help would be appreciated.

Homework Statement Find the equation of the line that is perpendicular to the tangent line to the curve, y=(3x+1)/(4x-2) at the point (1,2) Homework Equations The Attempt at a Solution I am absolutely confused with this problem. I tried taking a derivative of the equation. And I...

Homework Statement Find the equation of a tangent line at the curve at point (-3√3, 1) x^(1/3) + y^(1/3) = 4Homework Equations Point-slope: y-1=m(x-1) The Attempt at a Solution I took the derivative of that equation and resulted in -y^(2/3)/x^(2/3) When I tried plugging in x and y to...

A triangle ABC, where ,<A = 60 degrees. Let O be the inscribed circle of triangle ABC, as shown in the figure. Let D, E, and F be the points at which O is tangent to the sides AB, BC and CA. And let G be the point of intersection of the line segment AE and the circle O. (but AE line not cross...

Equation of tangent line (rec. form) to a polar curve! Homework Statement Quesiton: Find the rectangular form of the equation of the tangent line to the polar curve r=cos^3(theta) at the point corresponding to theta=pi/4 Homework Equations The Attempt at a Solution How to...

Homework Statement A curve is given by the equation: y^3+1004=(e^x+1)^2 Find the slope of the tangent line at the point (0,-10). Homework Equations The Attempt at a Solution I took the derivative of ((e^x+1)^2-1004)^(1/3) and that is (2e^x(1+e^x))/(3((1+e^x)^2-1004)^(2/3)) but...

Homework Statement Find the slope of the tangent line to the curve of intersection of the vertical plane x - y + 1 =0 and the surface z = x2+y2 at the point (1, 2, 5) Homework Equations Gradients, Cross products The Attempt at a Solution I'm pretty lost here. I think I have to...

I was working on a problem, and in my solution I came across a situation which I will try and state in the following question: Given two functions, f(x) and g(x), how would you find a line such that the line is tangent to f(x) at some point x=a, and tangent to g(x) at some point x=b, assuming...

Homework Statement If the line tangent to the graph of the function f at the point (1,7) passes through the point (-2,-2), then f'(1) is? Answer: 3 Homework Equations The Attempt at a Solution I got the right answer, but I think it was by pure luck. I found the slope...

Homework Statement Write an equation of each horizontal tangent line to the curve. Homework Equations y = 2y^3 + 6x^2y - 12x + 6y = 1 y' = (4x - 2xy) / x^2 + y^2 + 1) The Attempt at a Solution Well, horizontal tangent line means the derivative equals zero. Thus, 4x - 2xy = 0...

We know that the slope of the tangent line at a point on a curve is found by evaluating the derivative of the curve at that point. Say we have the curve y=2x. Say I wanted to find the tangent line at x=4 dy/dx=2 The first derivative is a constant, which is not surprising since the curve is...

Homework Statement There are infinitely many points on the curve y = \frac{sin x}{\sqrt{2}- cos x} at which the tangent line to this curve is horizontal. Find the x- and y-coordinates of one such point. Homework Equations y' = slope of the tangent line Etc., etc. The Attempt at a...

Find which value of x...horizontal Tangent Line Homework Statement What is given is F(x)= -4/(x-3)(x+4) and the problem asks for to find the value of x where f(x) has a horizontal tangent line.Homework Equations I read somewhere else on these forms that using the quotient rule is the key, and...

Homework Statement Find all points on the curve x^2 * y^2 + xy = 2 where the slope of the tangent line is -1. Homework Equations y' = -1 The Attempt at a Solution I got the y' = [ -2xy^2 - y ] / [ 2x^(2)y + x ] to be the gradient which I am sure is right. Then I subbed in y' =...

suppose the function F is define by F(x)=[integral from 1 to √x] (2t-1)/(t+2)dt for all real numbers x≥0 A.) evaluate F(1) B.) Evaluate F'(1) C.)Find an equation for the tangent line to the graph of F at the point where x=1 D.) on what intervals is the function F increasing? justify your...

Homework Statement Find the parametric equations of the line tangent to the curve of intersection of the paraboloid z = x² + y² and the ellipsoid 4x² + y² + z² = 9 at the point ( -1, 1, 2 ). Homework Equations Probable use of the gradient vector (as this is the chapter we are in)...

Homework Statement find the slope of the tangent line of f at the given point. Homework Equations f(x)= x^3 + x at (2,10) The Attempt at a Solution I know how to get the answer using the power rule, but I want to know the algebraic way of doing it I get stuck at x^3 + x - 10/ x...

For what value of b is the line y = 10x tangent to the curve y = e^{bx} at some point in the xy-plane? y' = b*e^{bx} = 10x How can I solve for b here?

Homework Statement 4x^2 - xy + y^2 = 4 At what points is the tangent line to the above curve vector [1 1]T? (T means I transposed the vector) Homework Equations The Attempt at a Solution I have the gradient vector, but I'm conceptually lost about what to do after that.

Homework Statement Use implicit differentiation to find an equation of the tangent line to the cardioid at the point (0, 0.5). x2 + y2 = (2x2 + 2y2 - x)2Homework Equations Derivative rules point slope formula The Attempt at a Solution I got y' = [16x3-4x2+16xy2-4y2-4y2-8x2+2x] / [2y -...

Homework Statement Find points on curve y=sinhx where the tangent line has slope 2 Homework Equations The Attempt at a Solution y' = 1/(sqrt(1-x^2)) = 2 4 = 1/(1-x^2) 4-4x^2=1 x=sqrt(3/4) the actual answer should be x = +or- ln(2+sqrt(3))

Find the equation of the tangent line to the curve y=(lnx)^cosx at the point (pi/2, 1)? The Attempt at a Solution lny = cosx(ln(ln(x))) d/dx = -sinx(ln(ln(x))) + cosx/(ln(x)(x)) y' = y(-sinx(ln(ln(x))) + cosx/(ln(x)(x))) this is the part where I get stuck

Homework Statement Find the equation of the circle that passes through the point (3,-2) and tangent to the line y=3x+5 at (-1,2). Answer in standard form. Homework Equations d= |mx0+b-y0| ____________ sqrt(1+m2 is needed to find the radius of the circle (x-h)2+(y-k)2=r2...

Homework Statement Find the parametric equation for the line tangent to the curve: x=t^3-1, y=t^4+1, z=t at the point (26, 82, 3). Use the variable t for your parameter. Homework Equations The Attempt at a Solution dx/dt=3t^2, dy/dt=4t^3, dz/dt=1 I got then that...

To understand differentials better, I'm trying to use differentials dy and dx in the equation of the tangent line to the curve x^2 at point 3. Here is the equation of the tangent line to the curve x^2 at point 3: y=f'(3)(x-3)+f(3)=2(3)(x-3)+9=6(x-3)+9 But since we are dealing with the...

Homework Statement A curve is defined parametrically by x=sin3t, y=cos3t, 0≤ t ≤ 2pi. Find the equation of the line tangent to the curve at the point defined by t=2pi/9. Homework Equations The Attempt at a Solution ?

Homework Statement Find two points on curve y=x4-2x2-x that have a common tangent line. Homework Equations *the one stated above dy/dx = 4x3-4x-1 The Attempt at a Solution equation of a tangent line: y=mx+b (4x3-4x-1) = m at two different points? So there are two points for which...

Homework Statement Find the slope of the tangent line using a specific formula g(x)=3t-t2 at (0,0) Homework Equations Im told to use this equation by the book f(c+deltax) - f(c) Deltax The Attempt at a Solution Everytime i plug it in by way of the books style i...

Homework Statement Find the equation of the tangent line to f(t)=<cot(t),csc(t)> at the point (1/sq.rt of 3, 2/sq.rt of 3) Homework Equations n/a The Attempt at a Solution I started by finding the slope, y'/x', so I got csc(t)cot(t)/csc^2(t). I then used the equation of a line...

Hello - I've been stuck on this for a while now and I really need some help. Homework Statement Find the equations for all lines that are tangent to the circle x^2+y^2=2y and pass through the point (0,4).Homework Equations y=mx+b ax^2+bx+c=0The Attempt at a Solution From the given equation of...

How do I find this?

Homework Statement Find the equation of the tangent line to y=sqrt(25-x^2) at the point (4,3) Homework Equations The Attempt at a Solution (25-x^2)^1/2 1/2(25-x^2)^-1/2 (2x)1/2(25-x^2)^-1/2 x(25-x^2)^-1/2 I have no idea what to do or where to go after this... Please Help!

Homework Statement The ellipsoid 4x^2 + 2y^2 + z^2 = 16 intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1,2,2)Homework Equations x = x0 + at y = y0 + bt z = z0 + ct The Attempt at a Solution Well i know that x0,y0 and z0...

Homework Statement Implicit Differentiation:Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 at (-3*31/2,1) Homework Equations ? None? The Attempt at a Solution 2/3 * x-1/3 + 2/3y-1/3*y' = 0 then after a few...

Homework Statement Prove that a vertical line and a line going from a point on a parabola to the focus of the parabola form equal angles with the tangent line of the point on the parabola. Homework Equations Focus = 1/4a (maybe relevant) The Attempt at a Solution I know how to...

Homework Statement Determine the coordinates of the points on the graph of f(x) = \sqrt {2x+1} where the tangent line is perpendicular to the line 3x+y+4 = 0 Homework Equations f(x) = \sqrt {2x+1} 3x+y+4 = 0 The Attempt at a Solution For this, I was going to find the...

Homework Statement Find parametric equations for the tangent line at the point (\cos(\frac{4 \pi}{6}) ,\sin(\frac{4 \pi}{6}) ,\frac{4 \pi}{6}) ) on the curve x=\cos t,\ y=\sin t, \ z=t Homework Equations The Attempt at a Solution Took the derivative r'(t)=( -sint...

Homework Statement I've never seen such a problem before: Find the two straight lines that are perpendicular to y=0.25x and tanget to the curve f(x)=1/xHomework Equations y=0.25x ; f(x)=1/x The Attempt at a Solution Using the power rule, I found the derivatives of: f(x)=-x^{-2} and y=0.25...

Homework Statement Find the equation for the tangent line to the curve f(x) = 2x3 - 5x - 3 at x = 2 Homework Equations How do i start this? I'm really confused and have an assignment with a bunch of these questions due tomorrow by midnight... if someone could help me that would be...

Homework Statement I have a homework that i couldn't do :( can you explain it to me please ? the problem is : find all values of x=c so that the tangent line to the graph of f(x) af (c , f(c)) will be horizontal http://img13.imageshack.us/img13/4222/scan0002izs.jpg The Attempt...

Homework Statement Find the equation of the tangent line on the function, f(x) = X^{2}-4x+1, which is perpendicular to the line, x+2y=10. Homework Equations The Attempt at a Solution x+2y=10 2y = 10-x y=-1/2x+5 Slope of perpendicular is -1/2, so slope of tangent is 2. The...

Find the equation for the line that is tangent to the given formula if y = pi/2 when x = 0 Homework Equations (x+1)dy - [(1/2)secycscy]dx = 0 The Attempt at a Solution I tried to do this, and I got that dy/dx = 1 / (0*0), which is infinity. So... y = \infty?

Homework Statement Find an equation of the tangent line to this curve at the point (1, -2). Homework Equations The Attempt at a Solution 2y' = 3x^2+6x y' = 3x^2+6x y'=3/2x^2+3x y+2=3(x-1) y+2=3x-3 y=3x-5