What is the instantaneous rate of change of

Ben Shaffer

Ben Shaffer

Answered question

2022-03-17

What is the instantaneous rate of change of f(x)=(x23x)ex1 at x=0?

Answer & Explanation

nida0694ii5

nida0694ii5

Beginner2022-03-18Added 6 answers

The instantaneous rate of change is the value of f'(0) differentiate f(x) using the product rule
f(x)=g(x)h(x)f(x)=g(x)h(x)+h(x)g(x)
here g(x)=(x23x)g(x)=2x3
and h(x)=ex1h(x)=ex1ddx(x1)=ex1
f(x)=(x23x)ex1+ex1(2x3)
=ex1(x23x+2x3)=ex1(x2x3)
f(0)=e01(003)=3e1=3e

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