# How do you find the instantaneous rate of change for f ( x ) = x <mrow class="

How do you find the instantaneous rate of change for $f\left(x\right)={x}^{3}+1$ for x=1
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Charlee Gentry
The instantenous rate of change is equal to the derivative of your function evaluated at the particular x value:
${f}^{\prime }\left(x\right)=3{x}^{2}$
At x=1:
${f}^{\prime }\left(1\right)=3\left(1{\right)}^{2}=3$