find f(x) for the following function. then find f(4), f(0), and f(-7). f(x)= - 9x - 8 f(x)=□

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $f(x)=ax^n$, then $f'(x)=nax^{n - 1}$. For $f(x)=-9x-8$, the first term $-9x$ has $a=-9$ and $n = 1$, and the second term $-8$ (a constant) has a derivative of 0. For the term $-9x$: $f_1'(x)=1\times(-9)x^{1 - 1}=-9$. For the constant term $-8$: $f_2'(x)=0$. So $f'(x)=-9$.

Step2: Find $f'(4)$

Since $f'(x)$ is a constant function equal to $-9$, then $f'(4)=-9$.

Step3: Find $f'(0)$

Since $f'(x)=-9$ for all $x$, then $f'(0)=-9$.

Step4: Find $f'(-7)$

Since $f'(x)=-9$ for all $x$, then $f'(-7)=-9$.

Answer:

$f'(x)=-9$, $f'(4)=-9$, $f'(0)=-9$, $f'(-7)=-9$