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The function y = f(x) has relative minima where:

The function y = f(x) has relative minima where: Correct Answer f'(x) = 0 and f''(x) > 0.

Explanation:

Maxima/ Minima of a function y = f(x):

  • Relative (Local) maxima are the points where the function f(x) changes its direction from increasing to decreasing.
  • Relative (Local) minima are the points where the function f(x) changes its direction from decreasing to increasing.
  • At the points of relative (local) maxima or minima, f'(x) = 0.
  • At the points of relative (local) maxima, f''(x) < 0.
  • At the points of relative (local) minima, f''(x) > 0.

From the above definition it is clear that at the points of relative minima of a function y = f(x), the value of f'(x) = 0 and f''(x) > 0.

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