Multiple choice

The function f(x) = 2x2 - 3x2 - 36x + 2 has its maxima at

  1. x = - 2 only

  2. x = 0 only

  3. x = 3 only

  4. both x = - 2 and x = 3
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A Correct answer
Explanation

f(x) = 2x^3 - 3x^2 - 36x + 2. f'(x) = 6x^2 - 6x - 36. Setting f'(x) = 0 gives x^2 - x - 6 = 0, so (x-3)(x+2) = 0. Roots are x = 3 and x = -2. f''(x) = 12x - 6. f''(-2) = -24 - 6 = -30 (<0, maxima). f''(3) = 36 - 6 = 30 (>0, minima). Thus, maxima at x = -2.

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