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Application Of Derivatives

Question

Prove that the logarithmic function is increasing wherever it is defined.

Solution

Let $straight f left parenthesis straight x right parenthesis space equals space log space straight x$ $therefore space space space space space straight D subscript straight f space equals left parenthesis 0 comma space infinity right parenthesis$
Now, $straight f apostrophe left parenthesis straight x right parenthesis space equals space 1 over straight x greater than 0 space space space space space space for all space space space straight x space space space space element of space space space space left parenthesis 0 comma space space space infinity right parenthesis$
Logarithmic function is increasing wherever it is defined.