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If f:RR-> RR is a differentiable funct...

If ` f:RR-> RR ` is a differentiable function such that `f(x) > 2f(x) ` for all `x in RR ` and `f(0)=1, ` then

A

f(x) `gt e^(2x) " in " (0,oo)`

B

`f(x) lt e^(2x) " in " (0,oo)`

C

`f(x) ` is increasing in `(0,oo)`

D

f(x) is decreasing in `(0,oo)`

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The correct Answer is:
A, C
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RESONANCE-APPLICATION OF DERIVATIVES-Exersise-3 Part I
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  9. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

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  10. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

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  11. A cylindrica container is to be made from certain solid material with ...

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  12. Let f,g:[-1,2]rarr RR be continuous functions which are twice differen...

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  13. Let f: R to (0 ,oo)" and " g :R to R be twice differentiable function...

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  14. Which of the following options is the only INCORRECT combination ?

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  15. Which of the following options is the only CORRECT combination

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  16. Which of the following options is the only CORRECT combination ?

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  17. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

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  18. If f:RR-> RR is a differentiable function such that f(x) > 2f(x) f...

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  19. then

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  20. For every twice differentiable function f: R->[-2,\ 2] with (f(0))^...

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