For the function f(x) = 2x³ - 15x² + 36x + 11, at which value of x does the local maximum occur?

Model Answer & Options

Source: Extra Practice

x = 2

x = 3

x = 0

x = 5

Explanation

To find local maxima/minima, we first find f'(x) = 6x² - 30x + 36. Setting f'(x) = 0 gives x² - 5x + 6 = 0, so (x-2)(x-3) = 0, giving critical points x=2 and x=3. Using the second derivative test, f''(x) = 12x - 30. At x=2, f''(2) = 24 - 30 = -6 (negative), indicating a local maximum. At x=3, f''(3) = 36 - 30 = 6 (positive), indicating a local minimum. Thus, the maximum occurs at x=2.

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