How do you find the instantaneous rate of change of the function $x^3 +2x^2 + x$ when x=1?

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Answer 1 · 2016-02-06T03:10:15

$8$

Find the value of the derivative at $x=1$ :

To find the derivative of the function, use the power rule:

$f'(x)=3x^2+4x+1$

The instantaneous rate of change and slope of the tangent line at $x=1$ is:

$f'(1)=3(1)^2+4(1)+1=8$

How do you find the instantaneous rate of change of the function x^3 +2x^2 + xx^3 +2x^2 + x when x=1?