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Manipal MET2017MathematicsContinuity and Differentiability

If f(x)= array cc 3 x^2+12 x-1, & -1 x 2 37-x, & 2 x 3 array . , then

Options

  1. Af(x) is decreasing on [-1,2]
  2. Bf^ (2) does not exist
  3. Cf(x) has the maximum value at x=2
  4. DNone of the above

Correct answer

B. f^ (2) does not exist

Step-by-step solution

Given, f(x)= array r 3 x^2+12 x-1,-1 x 2 37-x, 2 x 3 array . On differentiating, we get array ll & f^ (x)= array cc 6 x+12, & -1 x 2 -1, & 2 x 3 array . & f^ (x) 0 for -1 x 2 array f(x) is increasing in [-1,2] _ x 2⁺ f^ (x)=-1 and _ x 2⁻ f^ (x)=24 f^ (2) does not exist.

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