Question

question given the table of values below, find h(3) if h(x)=g(x)·f(x).

Explanation:

Step1: Apply product - rule

The product - rule states that if $h(x)=g(x)\cdot f(x)$, then $h^{\prime}(x)=g^{\prime}(x)f(x)+g(x)f^{\prime}(x)$.

Step2: Substitute $x = 3$

We need to find $h^{\prime}(3)$. Substitute $x = 3$ into the product - rule formula. When $x = 3$, we know that $f(3)=1$, $f^{\prime}(3)=4$, $g(3)= - 8$, and $g^{\prime}(3)=2$.
\[h^{\prime}(3)=g^{\prime}(3)f(3)+g(3)f^{\prime}(3)\]

Step3: Calculate the value

\[h^{\prime}(3)=(2)\times(1)+(-8)\times(4)\]
\[h^{\prime}(3)=2-32\]
\[h^{\prime}(3)=-30\]

Answer:

$-30$