If the tangent line to y = f(x) at (3, 2) passes through the point (0, 1), find f(3) and f '(3).

Question

If the tangent line to y = f(x) at (3, 2) passes through the point (0, 1), find f(3) and f '(3).

f(3)=_____

f'(3)=_____

Answer 1

Simon, you are given f(3) in the problem.

f'(3) is just the slope of the line connecting the 2 points (0,1) and (3,2).

Answer 2

a) Clear that f(3) = 2 since point (3, 2) is tangent point.

b) Now equation of tangent line at this poin: y - 2 = f'(3)(x - 3);

This line passes through point (0, 1). It give us: 1 - 2 = f'(3)(0 - 3). So, f'(3) = 1/3