a) Find an equation on the tangent line to the graph of y=g(x) at x= 5 if g(5) = -3 and g'(5) = 4

b) If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)

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- Nov 22nd 2011, 08:43 AMangelamoniquetangent line problems
a) Find an equation on the tangent line to the graph of y=g(x) at x= 5 if g(5) = -3 and g'(5) = 4

b) If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4) - Nov 22nd 2011, 08:49 AMTheChazre: tangent line problems
Use the point slope formula...

$\displaystyle y - y_1 = m(x - x_1)$

The point $\displaystyle (x_1 , y_1) = (5, -3)$

The slope is 4. - Nov 22nd 2011, 08:51 AMPlatore: tangent line problems
- Nov 22nd 2011, 09:00 AMangelamoniquere: tangent line problems
Thank you, but can you also tell me how you figured that out?

- Nov 22nd 2011, 12:35 PMHallsofIvyRe: tangent line problems
They attended class! One of the basic

**definitions**of the derivative is that it is the slope of the tangent line. - Nov 22nd 2011, 01:53 PMTheChazRe: tangent line problems
I wasn't sure exactly how to approach that!

Indeed, the veracity/validity/whatever of the point slope formula should not be called into question at this juncture. So we're left with the task of finding a point and a slope, in order to determine the desired line.

Welp, g(5)=-3 means that (5, -3) is the point.

And you really DO need to know that the slope of the tangent is given by the derivative.