If $f(x)$ is differentiable and strictly increasing function, then the value of $\lim_{x \rightarrow 0}\frac{f\left( x^{2} \right) - f(x)}{f(x) - f(0)}$ is

Question

Dr. Abubacker · Accepted Answer

(c)
Here, $\lim_{x \rightarrow 0}\frac{f\left( x^{2} \right) - f(x)}{f(x) - f(0)} = \lim_{x \rightarrow 0}\frac{f^{'}\left( x^{2} \right).2x - f^{'}(x)}{f^{'}(x)}$
$= \frac{- f^{'}(0)}{f^{'}(0)} = - 1$

Q. If $f(x)$ is differentiable and strictly increasing function, then the value of $\lim_{x \rightarrow 0}\frac{f\left( x^{2} \right) - f(x)}{f(x) - f(0)}$ is

Explanation

Reviewed by Dr. Abubacker

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