Question

question
if $f(-9)= - 4$, and $g(x)=6f(x)$, what is $g(-9)$?
do not include \$g(-9)=$\ in your answer. for example, if you found $g(-9)$
provide your answer below:

Explanation:

Step1: Apply constant - multiple rule of differentiation

The constant - multiple rule states that if $g(x)=cf(x)$ where $c$ is a constant, then $g^{\prime}(x)=cf^{\prime}(x)$. Here $c = 6$, so $g^{\prime}(x)=6f^{\prime}(x)$.

Step2: Substitute $x=-9$

We know that $f^{\prime}(-9)=-4$. Substitute $x = - 9$ into $g^{\prime}(x)=6f^{\prime}(x)$. Then $g^{\prime}(-9)=6\times f^{\prime}(-9)$.

Step3: Calculate the value

Substitute $f^{\prime}(-9)=-4$ into the equation $g^{\prime}(-9)=6\times f^{\prime}(-9)$. So $g^{\prime}(-9)=6\times(-4)=-24$.

Answer:

-24