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If {f}:{R}{{R}}is a differentiable function such that {{f}^{{{

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If $f : R R$ is a differentiable function such that $f^{p r i m e} (x) > 2 f (x) f or a l l x R a n d f (0) = 1, t h e n :$ $f (x)$ is decreasing in $(0, \infty)$ $f^{p r i m e} (x) < e^{2 x} \in (0, \infty)$ $f (x)$ ="" is="" increasing="" in="" $(0, \infty)$ ="" $f (x) = > e^{2 x} \in (0, \infty)$ $>$

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f : R R

is a differentiable function such that

f^{p r i m e} (x) > 2 f (x) f or a l l x R a n d f (0) = 1, t h e n :

f (x)

is decreasing in

(0, \infty)

f^{p r i m e} (x) < e^{2 x} \in (0, \infty)

f (x)

="" is="" increasing="" in=""

(0, \infty)

=""

f (x) = > e^{2 x} \in (0, \infty)

>

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Question Text	If $f : R R$ is a differentiable function such that $f^{p r i m e} (x) > 2 f (x) f or a l l x R a n d f (0) = 1, t h e n :$ $f (x)$ is decreasing in $(0, \infty)$ $f^{p r i m e} (x) < e^{2 x} \in (0, \infty)$ $f (x)$ ="" is="" increasing="" in="" $(0, \infty)$ ="" $f (x) = > e^{2 x} \in (0, \infty)$ $>$
Answer Type	Video solution: 1
Upvotes	150