1
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Question

# The total number of local maxima and local minima of the function f(x)={(2+x)3,−3<x≤−1x23,−1<x<2 is

A
2
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B
0
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C
3
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D
1
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Solution

## The correct option is A 2We have, f(x)={(2+x)3,−3<x≤−1x23,−1<x<2 ⇒f′(x)=⎧⎨⎩3(x+2)2.−3<x≤123x−13;−1<x<2 Clearlyf′(x) changes its sign at x=–1 from +ve to –ve and so f(x) has local maxima at x=–1. lso f′(0) does not exist but f′(0−)<0 and f′(0+)>0 , it can only be inferred that f(x) has a possibility of a minima at x=0. Hence the given function has one local maxima at x=–1 and one local minima at x=0.

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