equation of the tangent line

jvignacio · #1 $Old$ 11-20-2008, 04:29 AM

Find an equation for the line tangent to the graph of y = x^2at (3,9).

what are the steps to solving this problem? thank u

Twig · #2 $Old$ 11-20-2008, 06:16 AM

Hi!

First you need to find the derivative of your function $y = x^2$
$\frac{dy}{dx} = 2\cdot x$ .
You then insert the x-value into your derivative:
$y'(3) = 2 * 3 = 6$

Now you can use the following formula:
$(y-y_{1}) = k(x-x_{1}) \mbox{ where }y_{1} = 9 \; \; \; x_{1} = 3 \; \; \; k = 6$

After simplification you end up with:
$y = 6x -9$

This is is equation for tangent line at (3,9).