What is the instantaneous rate of change of $f(x)=(x^2-2)e^(x+2 )$ at $x=1$ ?

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Answer 1 · 2016-03-09T20:24:20

$f'(1)=e^3$

The instantaneous rate of change is the same as the derivative of the function.

We need the product rule to differentiate this function and using it gives

$f'(x)=(x^2-2)e^(x+2)+2xe^(x+2)$

$therefore f'(1)=(1-2)e^3+2e^3$

$=e^3$

What is the instantaneous rate of change of f(x)=(x^2-2)e^(x+2 ) f(x)=(x^2-2)e^(x+2 ) at x=1 x=1 ?