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Statement-1 . The critical points of f(x...

Statement-1 . The critical points of f(x)=xcosx occur in `(pi//4,pi//3)`
Statement-2 : The functions g(x)=xtanx increase ion `(0,pi//2)`

A

Statement-1 is True, Statement-2 is True,Statement -2 is a correct explanation for Statement -3

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:
B
It is given that g(x)=xtanx
`therefore g'(x)=xsec^2x+tanx gt 0 " for all " x in (0,pi//2)`
`rArr` is increasing on `(0,pi//2)`
So, statement-2 is true
Now, f(x)=x cosx
`rArrf'(x)=cosx-xsinx rArrf'(x)=cosx(1-xtanx)`
`rArr f'(pi/4)=1/sqrt2(1-pi/4) and f'(pi/3)=1/2(1-pi/sqrt3)`
`rArr f'(pi/4)gt0 and f'(pi/3)lt0` Also , f'(x) is a continuous function . So, f'(x)=0 for some `c in (pi//4,pi//3)`
So , both the statements are true but statements -2 is not a correct ecplanations of statements -1
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