Question

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

f(x) = 5 + \frac{3}{x}

f’(x) = -\frac{3}{x^2}

f’(1) = -3 (type an integer or a simplified fraction.)

f’(2) = -\frac{3}{4} (type an integer or a simplified fraction.)

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

Explanation:

Step1: Recall the derivative formula

We know that \( f'(x) = -\frac{3}{x^2} \) from the given information.

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

Substitute \( x = 3 \) into \( f'(x) = -\frac{3}{x^2} \), we get \( f'(3) = -\frac{3}{3^2} \).

Step3: Simplify the expression

Simplify \( 3^2 = 9 \), so \( f'(3) = -\frac{3}{9} = -\frac{1}{3} \).

Answer:

\( -\frac{1}{3} \)