Question

use the chart to find $h(5)$ in simplest form.
$h(x)=\frac{f(x)}{g(x)}$

Explanation:

Step1: Apply the quotient rule

The quotient rule states that if \(h(x)=\frac{f(x)}{g(x)}\), then \(h'(x)=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}\).

Step2: Substitute \(x = 5\) into the quotient - rule formula

We know that \(f(5)=-8\), \(f'(5)=-3\), \(g(5)=-11\), and \(g'(5)=3\).
Substitute these values into \(h'(x)=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}\):

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Answer:

\(\frac{57}{121}\)