Question

question given the following table of values, find $h(-6)$ if $h(x)=-7x + f(x)g(x)$. provide your answer below. $h(-6)=\square$
\begin{array}{|c|c|c|c|c|}hline x&f(x)&g(x)&f(x)&g(x)\hline - 6&-8&3&1&4\hline - 7&6&2&1&-8\hline - 8&-2&1&5&-5\hline 2&2&4&0&-4\hlineend{array}

Explanation:

Step1: Apply sum - product rule of differentiation

The sum - product rule states that if $h(x)=-7x + f(x)g(x)$, then $h'(x)=-7 + f'(x)g(x)+f(x)g'(x)$.

Step2: Substitute $x = - 6$

From the table, when $x=-6$, $f(-6)=-8$, $g(-6)=3$, $f'(-6)=1$, $g'(-6)=4$.
Substitute these values into $h'(x)$:
$h'(-6)=-7+(1\times3)+(-8\times4)$.

Step3: Calculate the value

First, calculate the products: $1\times3 = 3$ and $-8\times4=-32$.
Then, $h'(-6)=-7 + 3-32$.
Combine like - terms: $-7+3=-4$, and $-4-32=-36$.

Answer:

$-36$