Given a function:
[tex]y(x)=4x^2+1[/tex]
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,
[tex]\begin{gathered} \text{ROC}=y^{\prime}(x) \\ =8x+0 \\ =8x \end{gathered}[/tex]
at x = 1, the rate of change is:
[tex]\text{ROC}=8(1)=8[/tex]
