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Let f(x)=2sinx+tax-3x Statement-1: f(x...

Let f(x)=2sinx+tax-3x
Statement-1: f(x) does not attain extreme in `(-pi//2,pi//2)`
Statement-2 : f(x) is strictly increasing on `(-pi//2,pi//2)`

A

Statement-1 is True, Statement-2 is True,Statement -2 is a correct explanation for Statement -4

B

Statement -1 True ,Statement -2 is True ,Stament -2 is not a correct explanation for Statement -!

C

Statement -1 is True Statement -2 is False

D

Statement -1 is Flase,Statement -2 is True

Text Solution

Verified by Experts

The correct Answer is:
A
We have
f(x)=2sinx+tanx-3x
`rArr f'(x)=2cosx+sec^2x-3`
`rArr f'(x)=(-3cos^2x+2cos^3x+1)/(cos^2x)`
`rArr f'(x)=((1-cosx)^2(1+2cosx))/(cos^2x)gt 0, x in (-pi//2,pi//2)-[0]`
Son , f(x) is stricly increasing on `(-pi//2,0)cup(0,pi//2)`
Also , f'(0)=0
Hence , x=0 is the point of inflextion of f(x)
Thus , both statements are true and statement -2 is a correct explanations of statement-1
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