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

Explanation:

Step1: Recall the derivative formula

We know that \( f'(x)=-\frac{3}{x^2} \). To find \( f'(2) \), we substitute \( x = 2 \) into the derivative function.

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

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

Step3: Calculate the value

Calculate \( 2^2 = 4 \), so \( f'(2)=-\frac{3}{4} \).

Answer:

\( -\frac{3}{4} \)