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A function `g(x)` is defined as `g(x)=1/4f(2x^2-1)+1/2f(1-x^2)a n df(x)` is an increasing function. Then `g(x)` is increasing in the interval. `(-1,1)` `(-sqrt(2/3),0)uu(sqrt(2/3),oo)` `(-sqrt(2/3),sqrt(2/3))` (d) none of these

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BANSAL-APPLICATION OF DERIVATIVE-All Questions
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  2. f(x)=(x-2)|x-3| is monotonically increasing in (a)(-oo,5/2)uu(3,oo)...

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  3. A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2)a n df(x) ...

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  4. Let f(x)=1-x-x^3.Find all real values of x satisfying the inequality,...

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  5. The intervals of increase of f(x) defined by f(x)=int(-1)^x(t^2+...

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  6. If mean value theorem holds good for the function f(x)=(x-1)/x on ...

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  7. Let f(x)a n dg(x) be two continuous functions defined from RvecR , suc...

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  8. Find the critical points of the function f(x)=2/3sqrt(x^3)-x/2+int1^x(...

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  9. Let f(x)=x+\ sqrt(x)\ "o n"\ [1,4]dot The mean value theorem say...

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  10. Consider f(x)=|1-x|\ \ 1\ lt=xlt=2\ a n d\ \ g(x)=f(x)+bsinpi/2\ ...

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  11. If f is a continuous function on [0,1], differentiable in (0, 1) such ...

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  12. If the function f(x)=2x^2 + 3x + 5 satisfies LMVT at x = 2 on the clo...

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  13. Consider the function f(x)=8x^2-7x+5 on the interval [-6,6]dot Find th...

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  14. Range of the function f(x)=(ln x)/(sqrt(x)) is (a)(-oo,\ e) (b) (-o...

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  15. IF f(x)=x^3+a x^2+b x+5sin^2x\ is a strictly increasing functio...

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  16. In which one of the following intervals Rolles theorem hold(s) good...

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  18. The set of values of p for which the equation |lnx| -px =0 possess thr...

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  19. If f(x)=1+x+int1^x(ln^2t+2lnt) dt then f(x) increases in

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  20. Let f(x)={{:(x^(alpha)sin\ (1/x)sinpix\ \ \ ;\ \ x\ !=0),( 0\ \ \ \...

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