Question

for each problem find the instantaneous rate of change of the function at the given value ...Thank you and God Bless

Answer 1

The instantaneous rate of change of the function at the given value is -2.

`f^(\prime)(0)=-2`

Step-by-step explanation:

The instantaneous rate of change of the function at point x=a can be written as;

`f^(\prime)(a)=(df(a))/(dx)`

For the given function;

`y=2x^2-2x+2`

Then the derivative of the function is;

`f^(\prime)(x)=y^(\prime)=4x-2`

substituting x=0, we have;

`\begin{gathered} f^(\prime)(0)=4(0)-2 \\ f^(\prime)(0)=-2 \end{gathered}`

Therefore, the instantaneous rate of change of the function at the given value is -2.

`f^(\prime)(0)=-2`