Question

use the four-step process to find f’(x) and then find f’(1), f’(2), and f’(3).

f(x) = -x² + 6x - 3

f’(x) = -2x + 6

f’(1) = 4 (type an integer or a simplified fraction.)

f’(2) = 2 (type an integer or a simplified fraction.)

f’(3) = □ (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the derivative function

We know that \( f'(x)= -2x + 6 \).

Step2: Substitute \( x = 3 \) into \( f'(x) \)

Substitute \( x = 3 \) into \( f'(x)=-2x + 6 \), we get \( f'(3)=-2\times3 + 6 \).

Step3: Calculate the value

First, calculate \( -2\times3=-6 \), then \( -6 + 6 = 0 \).

Answer:

\( f'(3)=0 \)