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

Explanation:

Step1: Recall the derivative function

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

Step2: Substitute \( x = 1 \) into \( f'(x) \)

Substitute \( x = 1 \) into \( f'(x)=-\frac{3}{x^2} \), we get \( f'(1)=-\frac{3}{1^2} \).

Step3: Simplify the expression

Since \( 1^2 = 1 \), then \( -\frac{3}{1^2}=-3 \).

Answer:

\( -3 \)