Question

use the chart to find ( h(4) ) in simplest form.

h(x)=f(g(x))

answer

( h(4)= )

Explanation:

Step1: Apply the chain rule

The chain rule states that if \(h(x) = f(g(x))\), then \(h'(x)=f'(g(x))\cdot g'(x)\).

Step2: Substitute \(x = 4\)

When \(x = 4\), we first find \(g(4)\) from the table. \(g(4)=3\). Then \(h'(4)=f'(g(4))\cdot g'(4)\).

Step3: Use the table values

Since \(g(4) = 3\), \(f'(g(4))=f'(3)\) and \(g'(4) = 7\). From the table, \(f'(3)=1\). So \(h'(4)=f'(3)\cdot7\).

Step4: Calculate the result

Substitute \(f'(3) = 1\) into the expression. \(h'(4)=1\times7\).

Answer:

\(7\)