Question

question if $f(-3)=-10$, and $g(x)=-8f(x)$, what is $g(-3)$? do not include \$g(-3)=$\ in your answer. for example, if you found $g(-3)=7$, you would provide your answer below:

Explanation:

Step1: Apply the 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 $c = - 8$ and $g(x)=-8f(x)$. So $g^{\prime}(x)=-8f^{\prime}(x)$.

Step2: Substitute $x = - 3$

We know that $f^{\prime}(-3)=-10$. Substitute $x=-3$ into $g^{\prime}(x)=-8f^{\prime}(x)$. Then $g^{\prime}(-3)=-8\times f^{\prime}(-3)$.

Step3: Calculate the value of $g^{\prime}(-3)$

Substitute $f^{\prime}(-3)=-10$ into the equation $g^{\prime}(-3)=-8\times f^{\prime}(-3)$. So $g^{\prime}(-3)=-8\times(-10)=80$.

Answer:

80