Question

find the instantaneous rate of change for the function at the given value. g(t)=3 - t² at t = - 4 the instantaneous rate of change at t = - 4 is

Explanation:

Step1: Find the derivative of the function

The derivative of $g(t)=3 - t^{2}$ using the power - rule. The power rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. For $g(t)$, the derivative $g^\prime(t)$ of the constant 3 is 0, and the derivative of $-t^{2}$ is $-2t$. So, $g^\prime(t)=-2t$.

Step2: Evaluate the derivative at the given point

We want to find the instantaneous rate of change at $t=-4$. Substitute $t = - 4$ into $g^\prime(t)$. So, $g^\prime(-4)=-2\times(-4)$.
$g^\prime(-4)=8$

Answer:

8