Thread: tangent 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)

Use the point slope formula...



The point

The slope is 4.

Originally Posted by angelamonique

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)

The tangent line at is

Thank you, but can you also tell me how you figured that out?

They attended class! One of the basic definitions of the derivative is that it is the slope of the tangent line.

Originally Posted by HallsofIvy

They attended class! One of the basic definitions of the derivative is that it is the slope of the tangent line.

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.