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For all x in [1, 2] Let `f"(x)` of a non-constant function `f(x)` exist and satisfy `|fprimeprime(x)|<=2.` If `f(1)=f(2)`, then (A) There exist some `a in (1,2)` such that f'(a)=0 (B) f(x) is strictly increasing in (1,2) (C) There exists atleast one `c in (1,2)` such that `f'(c)>0` (D) `|f'(x)| lt 2 AA x in [ 1,2]`

A

There exist some `a in (1,2)` such that f(a)=0

B

f(x) is strictly increasing in (1,2)

C

There exist atleast one `c in (1,2)` such that `f(c) gt 0`

D

`|f'(x)|lt 2 AA x in [1,2]`

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The correct Answer is:
A, C, D
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RESONANCE-APPLICATION OF DERIVATIVES-Exersise-2 Part III
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  10. If f(x)=x/(1+x tan x): x in (0,pi/2), then

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  17. Which of the following statements are true :

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