use the chart to find $h(2)$ in simplest form.\n|$x$|$f(x)$|$f(x)$|$g(x)$|$g(x)$|\n|----|----|----|----|----|…

use the chart to find $h(2)$ in simplest form.\n|$x$|$f(x)$|$f(x)$|$g(x)$|$g(x)$|\n|----|----|----|----|----|\n|$2$|$6$|$5$|$- 12$|$-5$|\n$h(x)=-2f(x)$\nanswer attempt 1 out of 2\n$h(2)=$

use the chart to find $h(2)$ in simplest form.\n|$x$|$f(x)$|$f(x)$|$g(x)$|$g(x)$|\n|----|----|----|----|----|\n|$2$|$6$|$5$|$- 12$|$-5$|\n$h(x)=-2f(x)$\nanswer attempt 1 out of 2\n$h(2)=$

Answer

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:

$-10$