The total number of local maxima and local minima of the function f(x)={(2+x)3,−3<x≤−1x2/3,−1<x<2 is
A
0
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B
1
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C
2
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D
3
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Solution
The correct option is C 2 f(x)=(2+x)3,−3=x2/3,−1f′(x)=3(2+x)2,−3=2/3x−1/3,−1, clearly x=−2 is extremum and at x=−1, f(x) is not differentiable Hence there is 2 maximum or minimum point.