How many points in the interval [-a, a] does the

dolovatgyp

dolovatgyp

Answered question

2022-04-21

How many points in the interval [-a, a] does the instantaneous rate of change of f equal the average rate of change of f if f(x)=ex2?

Answer & Explanation

Sergio Kidd

Sergio Kidd

Beginner2022-04-22Added 14 answers

Average rate of change of f on [-a, a] is
f(a)-f(-a)a-(-a)=ea22a=0
The instantaneous rate of change of f at x is
f(x)=2xex2
So the question becomes:
How many solutions to 2xex2=0 are there in [-a, a].
The answer is one (namely x=0).

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