F- 0- - R is continuous- If Fx is a differentiable function such that Fx- fx- - x-0 and f x 2 - x 2 - x 3- then f4 equals

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Complex Numbers

f: 0,∞ → R is...

Question

$f : (0, \infty) \to R$ is continuous. If $F (x)$ is a differentiable function such that $F (x) = f (x), \forall x > 0$ and $f (x^{2}) = x^{2} + x^{3}$ , then $f (4)$ equals

12

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7

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Solution

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Similar questions

f (x)

f^{'} (4) = 5

lim x \to 2 \frac{f (4) - f (x^{2})}{x - 2}

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f^{'} (4) = 5

{lim}_{x \to 2} \frac{f (4) - f (x^{2})}{x - 2}

f : R \to R

f (x) - 2 f (\frac{x}{2}) + f (\frac{x}{4}) = x^{2}

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F (x) = \int_{0}^{x} f (t) d t

F (x^{2}) = x^{2} (1 + x)

f (4)

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lim x \to 0 \frac{f (4 x) - 3 f (3 x) + 3 f (2 x) - f (x)}{x^{3}} = 12

f^{'''} (0)

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