evaluate the derivative of the function at the given point. f(s)= - 6√s - 9, a = 9 f(9)= (simplify your…

Explanation:

Step1: Rewrite the function

Rewrite $f(s)= - 6\sqrt{s}-9$ as $f(s)=-6s^{\frac{1}{2}} - 9$.

Step2: Apply power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For $f(s)=-6s^{\frac{1}{2}}-9$, the derivative $f^\prime(s)=-6\times\frac{1}{2}s^{\frac{1}{2}-1}-0=-3s^{-\frac{1}{2}}$.

Step3: Evaluate the derivative at $s = 9$

Substitute $s = 9$ into $f^\prime(s)$. We get $f^\prime(9)=-3\times9^{-\frac{1}{2}}=-3\times\frac{1}{\sqrt{9}}=-3\times\frac{1}{3}=-1$.

Answer:

$-1$