Question

use the chart to find $h(2)$ in simplest form.

$x$	$f(x)$	$f(x)$	$g(x)$	$g(x)$

$h(x)=-2f(x)$
answer attempt 1 out of 2
$h(2)=$

Explanation:

Step1: Apply constant - multiple rule of differentiation

The constant - multiple rule states that if $h(x)=cf(x)$ where $c$ is a constant, then $h^{\prime}(x)=cf^{\prime}(x)$. Here $c = - 2$ and $h(x)=-2f(x)$, so $h^{\prime}(x)=-2f^{\prime}(x)$.

Step2: Substitute $x = 2$

We know from the table that $f^{\prime}(2)=5$. Substitute $x = 2$ into $h^{\prime}(x)=-2f^{\prime}(x)$. Then $h^{\prime}(2)=-2\times f^{\prime}(2)$.

Step3: Calculate the value

Substitute $f^{\prime}(2) = 5$ into the equation $h^{\prime}(2)=-2\times f^{\prime}(2)$. We get $h^{\prime}(2)=-2\times5=-10$.

Answer:

$-10$