Suppose an equation of the tangent line to the curve y = f(x) at the point where a = 2 is y = 9x − 3.

Question

1. Find f(2)
2. Find f '(2)

Answer 1

1. Find f(2)= 15
2. Find f '(2)=9

Answer 2

The function and the tangent line have the same value at x = 2.

Assuming that y = 9x – 3 is the tangent line (the post is worded a bit unclearly), then we have

the answer to question 1:

f (2) = 9(2) – 3 = 15

The function and the tangent line also have the same slope at x = 2.

Since the slope of the tangent line is 9, the slope of the function at x = 2 is also 9.

So we have the answer to question 2:

f '(x) = 9.

BTW, I'm basically just providing an explanation here of the correct answers given earlier by Billy M.

Answer 3

From the strangely written post I am assuming that the equation of the tangent line at x =2 is

y = 9x - 3, that is f'(x) = 9x - 3 at x = 2.

Therefore f'(2) = 9(2) - 3

If f'(x) = 9x - 3, then f(x) = 4.5x² - 3x + C.

f(2) = 4.5(2)² - 3(2) + C