Using the definition of the derivative, find f prime (x). Then find f prime (1) , f prime (2) , and f prime (3) when the derivative exists.

Step-by-step explanation:

We need the function f (x) to be able to determine the required.

Suppose we were given a function

f (x) = y

f' (x) represents the first derivative of the function f (x) = y.

f' (1) represents the value of the first derivative of the function f (x) = y after replacing x by 1.

f' (5) represents the value of the first derivative of the function f (x) = y after replacing x by 5.

Example: Suppose f (x) = x² + 3x, find

f' (x), f' (1), and f' (5).

f' (x) = 2x + 3

f' (1) = 2 (1) + 3 = 5

f' (5) = 2 (5) + 3 = 13