Prove that the following functions do not have maxima or minima:

(ii)  g(x) = \log x

Answers (1)

Given function is
g(x) = \log x
g^{'}(x) = \frac{1}{x}\\ g^{'}(x) = 0\\ \frac{1}{x}= 0\\
Since log x deifne for positive x i.e. x > 0 
Hence,   by this, we can say that g^{'}(x)> 0 for any value of x
Therefore, there is no c \ \epsilon \ R such that  g^{'}(c) = 0
Hence, the function g(x) = \log x does not have either maxima or minima

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