Question

given the function f(x)= -\frac{3}{x}-3\sqrt{x}, find f(4). express your answer as a single fraction in simplest form.

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=-\frac{3}{x}-3\sqrt{x}$ as $f(x)= - 3x^{-1}-3x^{\frac{1}{2}}$.

Step2: Find the derivative

Using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, we have $f'(x)=(-3)\times(-1)x^{-2}-3\times\frac{1}{2}x^{-\frac{1}{2}}=\frac{3}{x^{2}}-\frac{3}{2\sqrt{x}}$.

Step3: Evaluate $f'(4)$

Substitute $x = 4$ into $f'(x)$:

$$
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$$

Answer:

$-\frac{9}{16}$