Question

Find the net change in the value of function $g\left(t\right)=1-t^2$for the inputs from $t=-2\mathrm{to}t=5$.

Short answer

The net change in the value of function is $g\left(5\right)-g\left(-2\right)=-21$.

Step-by-step solution

Step 1. Evaluate the value of function at extreme points.

From the given function,

$g\left(t\right)=1-t^2\mathrm{....}\left(1\right)$

Evaluate $g\left(-2\right)\text{and}g\left(5\right)$gives,

role="math" localid="1644530101793" $$\begin{gathered} g\left(-2\right)=1-{\left(-2\right)}^2\mathrm{....}\left(\text{Substitute}t=-2\text{in}\left(1\right)\right) \\ =-3 \\ g\left(5\right)=1-{\left(5\right)}^2\mathrm{....}\left(\text{Substitute}t=5\text{in}\left(1\right)\right) \\ =-24 \end{gathered}$$

Step 2. Obtain difference at extreme points.

Evaluate difference at extreme points gives the net change $f\left(b\right)-f\left(a\right)$where $b>a$. Therefore,

role="math" localid="1644530175337" $\begin{array}{c}g\left(5\right)-g\left(-2\right)=-24-\left(-3\right)\\ =-21\end{array}$

Step 3. Description of steps.

The net change in the value of function is $g\left(5\right)-g\left(-2\right)=-21$.