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Let g(x)=2f(x/2)+f(1-x) and f^(primeprim...

Let `g(x)=2f(x/2)+f(1-x)` and `f^(primeprime)(x)<0` in `0<=x<=1` then g(x)

A

decreases in `[0,(2)/(3)]`

B

decreases `[(2)/(3),1]`

C

increases in `[0,(2)/(3)]`

D

increases in `[(2)/(3),1]`

Text Solution

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The correct Answer is:
B, C
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RESONANCE-APPLICATION OF DERIVATIVES-Exersise-2 Part III
  1. Which of the following statements is//are correct?

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  2. If f(x) = 2x + cot^(-1) x + log ( sqrt(1+x^2 )-x) then f(x)

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  3. Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)

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  4. Let f(x)=x^(m/n) for x in R where m and n are integers , m even an...

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  5. Let f and g be two differentiable functions defined on an interval I s...

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  6. Let g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot Then prov...

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  7. if p,q,r be real then the interval in which f(x) =|underset(pr" ...

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  8. If f(x)=(x^2)/(2-2cosx);g(x)=(x^2)/(6x-6sinx) where 0 < x < 1, then (A...

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  9. 2/(x-f(pi/12))+3/(x-f(pi/4))+4/(x-f((5pi)/12))=0

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  10. Let f(x)=(x^2-1)^n(x^2+x+1) then f(x) has local extremum at x=1 whe...

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  11. If f(x)=x/(1+x tan x): x in (0,pi/2), then

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  12. If f(x)=alog|x|+b x^2+x has extreme values at x=-1 and at x=2 , then f...

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  13. if f(x) =[underset(-x " ", " " x gt 1) (-sqrt(1-...

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  14. if f(x) = tan^(1) x -(1//2) en x. then

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  15. Let f(x) =(40)/(3x^(4) +8x^(3) -18x^(2)+60). Which of the following ...

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  16. A function f(x) =(x^(2) -3x +2)/(x^(2)+ 2x -3) is

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  17. For the fucntion f(x) =x cot^(-1) x , x ge 0

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  18. Which of the following statements are true :

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  19. Let f(x) be a differentiable function and f(alpha)=f(beta)=0(alpha< be...

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  20. which of the following inequalities are valid-

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