Question

Estimate the instantaneous rate of change of y(x)=4x2+1 at the point x=1Your answer should be accurate to at least 2 decimal places.

Answer 1

Given a function:

`y(x)=4x^2+1`

We have to find the instantaneous rate of change of the function at x = 1.

We know that the instantaneous rate of change of the function is equal to the derivative of the function. so,

`\begin{gathered} \text{ROC}=y^(\prime)(x) \\ =8x+0 \\ =8x \end{gathered}`

at x = 1, the rate of change is:

`\text{ROC}=8(1)=8`