Find f(4) and f'(4), assuming that the tangent line to y= f(x) at a=4 is y= -6x + 2.

Question

Find f(4) and f'(4), assuming that the tangent line to y= f(x) at a=4 is y= -6x + 2.

f(4) = ?

f'(4) = ?

Answer 1

The tangent line and f(x) pass through the same point at x = 4

This point is (4, –6(4) + 2) = (4, –22), so f(4) is the y-coordinate of this point:

f(4) = –22

The tangent line at x = 4 is y = –6x + 2, so f'(4) is the slope of this line.:

f'(4) = –6

Answer 2

f(4) = -3(4)² + 2(4) + C

f'(4) = -6