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Theorems for Differentiability

3. Let f(x) b...

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3. Let f(x) be a strictly increasing and diffrentiable function. then find the limit

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f (x)

be a strictly increasing and differentiable function, then

lim x \to 0 \frac{f (x^{2}) - f (x)}{f (x) - f (0)}

Q. A differentiable function

f (x)

is strictly increasing

\forall x ϵ R

f (x)

is a differentiable function and

f (x) - x^{3}

is strictly increasing, then

f (x) + x - x^{2}

f : [0, \infty) \to [2, \infty)

be a differentiable increasing and onto function satisfying

f^{2} (x) - 2 f (x) - \sqrt{x} = f^{2} (y) - 2 f (y) - \sqrt{y}

g (x)

be the inverse of

f (x)

g^{'} (4)

What is the condition for a strictly increasing differentiable function?

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