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MathematicsSingle correct+3 / -1Question 6 of 69

IIT-JEE 2008 · Paper 1, Mathematics question 6

The total number of local maxima and local minima of the function
f(x)={(2+x)3,−3<x≤−1x2/3,−1<x<2f(x)=\begin{cases}(2+x)^3,&-3<x\le-1\\x^{2/3},&-1<x<2\end{cases}
is

Choose one option
Answer and worked solution

Official answer: C

On (−3,−1](-3,-1]: (2+x)3(2+x)^3 increases, reaching 1 at x=−1x=-1.

On (−1,2)(-1,2): x2/3x^{2/3} decreases from 1 (as x→−1+x\to-1^+) to 0 at x=0x=0, then increases.

Extrema.

  • x=−1x=-1: ff rises to 1 and then falls: local maximum.
  • x=0x=0: f=0f=0 with larger values on both sides (a cusp): local minimum.

Total: 2.

(C)

Topics:Maxima and minima
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