Question

find the instantaneous rate of change of the function at the given value . Thank you

Answer 1

Answer:

The instantaneous rate of change of the function at x=0 is 0

$f^{\prime}(0)=0$

Explanation:

We want to find the instantaneous rate of change of the function below;

$y=2x^2-2$

at x =0.

The instanteneous rate of change of function f(x) at point a can be written as;

$f^{\prime}(a)=\frac{df(a)}{dx}$

For the given function;

$f^{\prime}(x)=y^{\prime}=4x$

so, at x=0;

$\begin{gathered} f^{\prime}(x)=4x \\ f^{\prime}(0)=4(0) \\ f^{\prime}(0)=0 \end{gathered}$

Therefore, the instantaneous rate of change of the function at x=0 is 0

$f^{\prime}(0)=0$