What is the instantaneous rate of change of

Damian Hanna

Damian Hanna

Answered question

2022-03-15

What is the instantaneous rate of change of f(x)=xexx2ex at x=-1?

Answer & Explanation

Skyler Guzman

Skyler Guzman

Beginner2022-03-16Added 6 answers

The instantaneous rate of change of a function f(x) at a given point is the slope of the tangent line at that point, that is, the derivative f'(x) evaluated at that point.
In this case, we have
f(x)=xex+exx2ex2xex
=ex(x2+x1)
Then, evaluated at x=-1 we have
f(1)=e1((1)2+(1)1)
=1e(1)
=16

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