Tangent line Definition and 279 Threads

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.

Find the equations of the tangent lines to the graph of f(x) = \sin x at x = 0 and at x = \frac{ \pi }{3}. Use each tangent line to approximate \sin( \frac{ \pi }{6} ) . Would you expect these results to be equally accurate, since they are taken equally far away from x = \frac{ \pi }{6}...

Hey, right now in our calculus course we are currently working on "derivatives" using the differentiation equations. I was hoping that someone could help me out with the following question: Find the equation of the tangent line to the curve at the given point. y = rootX , (4, 0.4)...

can you guys help me how to do this problem? f(x) = 3x^2 - 1 (3,8) Find slope and tangent line, I have answer 6, is that right? and can you guys show the step to get the answer, thanks =) (tangent line i already know how to do) oh and this one, y = x^2 - 4 Find...

Hi, I need help on a math problem that asks me to find k such that the line is tangent to the function, givenf(x) = x^2 - kx and y = 4x - 9. I don't know how to solve for k. Is "tangent line" the same thing as the equation that is the derivative of the function?

I'm given f(x) = x^2 and g(x) = -x^2 + 2x - 5 And it says Let A (a, f(a)) be the point of tangency on f(x) and B (b, g(b)) be the point of tangency on g(x). Use calculus to find the slope of the tangent line at each point. What must be true about these two slope expressions? I know we...

really isn't calculus but that's the name of my class so, anyway I am having a problem here. i think its pretty simple I am just missing something. I am supposed to find the slope of the tangent line using one point and: slope of tangent line = \frac{f(a+h)-f(a)}{h} h\rightarrow0...

I have a homework problem as follows: If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4). Using the slope formula and the point-slope formula, I found that the equation of the given tangent line is y = 1/4x + 2. Now I want to find f(x) so I can...

Can someone check if I did this right: Find the equation of the tangent line to the graph of f(x) = \frac {2x-5}{x+1} at the point at which x = 0. f(x) = \frac {2(0) - 5}{(0) + 1} = -5 So I got y = -5 Then I wanted to find the derivative of the original using the quotient rule to find...

Can anybody help me out with this Q? "A curve R in space has vector equation: x = (sin(\pi u), u^2 - 1, u^2 + 3u + 3) u is a real number. Find a vector equation of the tangent line to R at the point (0, 0, 1)"

Am I thinking right about this following question: Give a geometric argument to show that the graph of y = lxl has no tangent line at the point (0,0). Since that graph would be basically the bisectors of the 1st and second quadrants, why can't the x-axis be that tangent line? (def. of a...

Okay so i have f(x) I want to find f'(x) it's derivative F'(x) is the slope So let's say they ask for the tangent line to the point on the graph where x=2. I replace x by 2 in my derived equation and isolate Y. Let's say i found that Y=5 Now I need to find the equation of the Tangent...

Find an equation of the tangent line to the curve with parametric equations x=tsint, y=tcost at the point (0,-π). went dy/dt / dx/dt --> cost - tsint/sint + tcost t not given so figured it could be: x=t(sin(1)) --> t= x/sin(1) or y=t(cos(1)) --> t= y/cos(1) wondering if...

Need Help Please! Tangent Line Problems! Hey, Okay, so here's the problem. I've got this quartic: 0 = -9x^4 + 190x^3 + 840x^2 + 1992x I need to find if this graph has two or more points with the same tangent line, and I'm at a loss. Given a point, I have no problem finding the tangent...

Find the y-intercept of the tangent line to the graph of y = (9)/sqrt(1 + x) at the point where x = 9. I used the quotient rule to find the derivative. I found that to be (-9/2(1+x)^-1/2)/(1+x) But then I am totally clued out... Thanks for helping me out. volc

Hello everyone, I'm having troubles seeing how this works. The directions are: Find parametric equations for the tagent line to the curve with the given parametric equations at the specified point. Here is my work and problem...

how do you find orientation of a line that is tangent to the particle's path at t = 2.10 s?(from the +x axis) before this i found the position r of a particle moving in an xy plane is given by r = (1.00t3 - 8.00t) i + (7.00 - 4.00t4) j. So I found r,v,a, for t=2.10s (all in m) r=-7.54 i...

Find parametric equations for the tangent line at the point (cos(-4pi/6),sin(-4pi/6),-4pi/6) on the curve x=cost, y=sint,z=t x(t) = _________ y(t) = _________ z(t) = _________ r'(t) = <-sin(t), cos(t), 1> r'(0) = <0,1,1> my answer: x = cos(-4pi/6) + 0t y = sin(-4pi/6) +1t z =...

I need to find an equation for the tangent line to the graph of the function at the specified point, I had some trouble simplifing f(x) so that I can take the lim as h->0 which is the slope. f(x) = Sqrt(x)/5 at (4,(2/5))

I need to find an equation for the tangent line to the graph of the function at the specified point, I had some trouble simplifing f(x) so that I can take the lim as x->0 which is the slope. f(x) = Sqrt(x)/5 at (4,(2/5))

Here's the problem: detrmine DE giving the slope of the tangent line at point (x,y) for the given family of curves: 2cy = x^2 - c^2 Here's what I have: slope of this curve: y' = \frac{x}{c} So, then the slope of tangent line is negative inverse: y' = \m \frac{-c}{x}...

i just want to check my answers...coz i don't have an answer key to compare with... 1) y^2-3xy+x^2=7 y'=3y-2x/2y-3x 2) x^2+y^2=2xy y'=1 3) 2x^2+xy+3y^2=0 y'=-4x-y/x+6y 4) 5x^2-2xy+7y^2=0 y'=y-5x/7y-x 5) 7x^2+6xy+9y^2=0 y'=-7x-3y/3x+9y 6) Find the equation of the tangent line...

Hello all Find the equations of all lines tangent to y = x^2 - 4 that pass through the point P(5,5) My solution: If f(x) = x^2 - 4 then f'(x) = 2x . So y - 5 = 10(x-5) This is just tthe equation of 1 tangent line. To find all tangent lines would I have to add some constant...

Find the equation of the tangent line at x=2 F(X)=2x+7x(e^(x-2)) I know you put 2 into find the y intercept and you take the derivative to find the slope. I get 2+(7e^(-2)x + 7e^-2)e^2 for my derivative and y=23x+18 as my answer and i know that is not correct.

Find the equations of the tangent line to the curve y= (x-1)/(x+1) that are parallel to the line x-2y=2 help!

Original question: a) Say r'(t) = 3t^2 i - cost j + 2t k, and r(0) = i + k. Find r(t). b) Find T(t). c) Find parametric equations for the tangent line to the curve at t=1. I have done parts a and b and got the following results: a) r(t) = t^3 + 1 i - sint j + t^2 + 1 k b)T(t) =...

Write the equation of the tangent line to the cure y=cosx at a=pi/4 (y-y1)=m(x-x1) cos(pi/4)=sqrt(2)/2 y'=-sinx=-sin(pi/4)=-sqrt(2)/2 (y-sqrt(2)/2)=m(x-pi/4) y'=-sqrt(2)/2(x-pi/4)+sqrt(2)/2 My teacher circled the y' and took a point off. I know that y'=-sinx but what should be in...

Here is exactly how the problem reads: 53. Find an equation of the tangent line to the graph of F at the indicated point. y = x^4 - 3x^2 + 2 (1,0) I'll be honest. I do not understand how to do these type problems. I've been reading this section of the book over and over to...

I need to know how to find the equation of the tangent line to the graph of the equation y = xe^(1/x^2) + ln(3 - 2x^2) at the point (1, e). Admittedly, I have no idea at all what the question is asking for and I don't have the slighest clue on how to solve this question. Any help will be greatly...