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Let g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3si...

Let `g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot` Then prove that `g` is increasing whenever is increasing.

A

`phi` is increasing wherever f is increasing

B

`phi` is increasing whenever f is decreasing

C

`phi` is decreasing whenever f is decreasing

D

`phi` is decreasing if `f(x)=-11`

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The correct Answer is:
A, D
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RESONANCE-APPLICATION OF DERIVATIVES-Exersise-2 Part III
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  3. Let f(x)=x^(m/n) for x in R where m and n are integers , m even an...

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

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

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

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

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  8. 2/(x-f(pi/12))+3/(x-f(pi/4))+4/(x-f((5pi)/12))=0

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

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

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

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

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

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

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  17. Which of the following statements are true :

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

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  19. which of the following inequalities are valid-

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  20. For all x in [1, 2] Let f"(x) of a non-constant function f(x) exist a...

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