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JEE Advanced2008MathematicsApplication of DerivativesActual

The total number of local maxima and local minima of the function f(x)= array lc (2+x)^3 ; & -3 < x -1 x^ 2 3 ; & -1 < x < 2 array . is

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

C. 2

Step-by-step solution

Given that, f(x)= array l (2+x)^3 ;-3 Clearly, f^ (x) changes its sign at x=-1 from + ve to -ve and so f(x) has local maxima at x=-1 . Also, 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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