Properties Of The Average Value Of A Function

Question

Let $$f$$ be a function that is continuous on the interval $$[0, 10]$$. All of the following statements are true EXCEPT:

Accepted Answer

The average value of $$f(x)$$ on [0,10] is necessarily attained at $$x=5$$, the midpoint of the interval.

Answer

According to the Mean Value Theorem for Integrals, there exists some $$c \in [0,10]$$ such that $$f(c)$$ equals the average value of $$f(x)$$ on [0,10].

Answer

Critical points, where $$f'(x)=0$$, are not required to coincide with the point where $$f(x)$$ equals its average value on [0,10].

Answer

The average value is computed as $$\frac{1}{10}\int_{0}^{10} f(x)\,dx$$.

Properties Of The Average Value Of A Function

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