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

Explanation:

Step1: Recall the derivative function

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

Step2: Substitute \( x = 2 \) into \( f'(x) \)

Substitute \( x = 2 \) into \( f'(x)=-2x + 6 \), we get \( f'(2)=-2\times2 + 6 \).

Step3: Calculate the value

First, calculate \( -2\times2=-4 \), then \( -4 + 6 = 2 \).

Answer:

\( f'(2)=2 \)