On which of the following intervals is the function f given byf(x) = x100 + sin x –1 strictly decreasing?

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None of these Explanation: Given f(x) = x100 + sin x - 1, f'(x) = 100 x99 + cos x (a) Interval 0 < x < 1, 0 < 100 x99 < 100 And cos x = + positive therefore f'(x) = + positive Hence, the function f is increasing. (b) Interval is pi/2 < "x" < pi therefore f'(x) = 100 x99 + cos x = + positive Hence, the function f is increasing. (c) Interval is, 0 < "x" < pi/2 Here, 100 x99 and cos x are both positive. therefore f'(x) = + ve Hence, the function f is increasing.

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