Question
Asked Jan 20, 2020
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Suppose that ƒ is continuous on [a, b] and that c is an interior point of the interval. Show that if ƒ′(x) <=0 on [a, c) and ƒ′(x)>= 0 on (c, b] , then ƒ(x) is never less than ƒ(c) on [a, b].

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Expert Answer

Step 1

Mean Value Theorem:

Calculus homework question answer, step 1, image 1
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Step 2

Given that f is continuous on [a, b] and c is an interior point of the interval [a, b].

Then f is continuous on [a, c) and on (c, b].

Calculus homework question answer, step 2, image 1
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Step 3

Also,

...
Calculus homework question answer, step 3, image 1
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