What is the instantaneous rate of change of f(x)=(x2−3x)ex at x=2?

Aryanna Rowland

Aryanna Rowland

Answered question

2022-03-16

What is the instantaneous rate of change of f(x)=(x23x)ex at x=2?

Answer & Explanation

orangepaperiz7

orangepaperiz7

Beginner2022-03-17Added 9 answers

The instantaneous rate of change when x=2 can be found through computing
f'(2).
To find f'(2), first find f'(x)
Use the product rule:
f(x)=exddx[x23x]+(x23x)ddx[ex]
f(x)=ex(2x3)+ex(x23x)
f(x)=ex(2x+3+x23x)
f(x)=ex(x2x+3)
f(2)=e2(222+3)
f(2)=5e2
f(2)=5e2
f(2)36.945

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