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6. Application of Derivatives
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Q10 of 168 Page 205

Prove that the logarithmic function is strictly increasing on (0, ∞).

The given function is f(x) = logx


It is clear that for x>0,


Therefore, f(x) = log x is strictly increasing in interval (0,∞).


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Find the values of x for which y = [x(x – 2)]2 is an increasing function.

9

Prove that is an increasing function of θ in

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Prove that the function f given by f (x) = x2 – x + 1 is neither strictly increasing nor strictly decreasing on (– 1, 1).

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Which of the following functions are strictly decreasing on ?

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Questions · 168
6. Application of Derivatives
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