Home
Class 12
MATHS
Let f and g be two differentiable functi...

Let f and g be two differentiable functions defined on an interval I such that `f(x)>=0` and `g(x)<= 0` for all `x in I` and f is strictly decreasing on I while g is strictly increasing on I then (A) the product function fg is strictly increasing on I (B) the product function fg is strictly decreasing on I (C) fog(x) is monotonically increasing on I (D) fog (x) is monotonically decreasing on I

A

The product function fg is strictly increasing on I

B

The product function fg is strictly decreasing on I

C

fog (x) is monotonically increasing on I

D

fog (x) is monotonically decreasing onI

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part IV comprehension|11 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-3 Part I|27 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part II|21 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

Let f and g be real valued functions defined on interval (-1, 1) such that g'' (x) is continuous, g(0) ne 0, g'(0) = 0, g''(0) ne 0, and f(x) = g''(0) ne 0 , and f(x) g(x) sin x . Statement I lim_( x to 0) [g(x) cos x - g(0)] [cosec x] = f''(0) . and Statement II f'(0) = g(0).

Let f and g be real valued functions defined on interval (-1,\ 1) such that g"(x) is continuous, g(0)!=0 , g'(0)=0, g"(0)!=0 , and f(x)=g(x)sinx . Statement-1 : ("Lim")_(x->0)[g(x)cotx-g(0)"c o s e c"x]=f"(0) and Statement-2 : f'(0)=g(0)

Let f (x) and g (x) be two differentiable functions, defined as: f (x)=x ^(2) +xg'(1)+g'' (2) and g (x)= f (1) x^(2) +x f' (x)+ f''(x). The value of f (1) +g (-1) is:

Let f(x) and g(x) be two continuous functions defined from R rarr R, such that f(x_(1))>f(x_(2)) and g(x_(1)) f(g(3 alpha-4))

Let f(x) be a differentiable function in the interval (0,2) , then the value of int_0^2 f(x) dx is :

Let f and g be two differential functions such that f(x)=g'(1)sin x+(g''(2)-1)xg(x)=x^(2)-f'((pi)/(2))x+f''((-pi)/(2))

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

Let f(x) be a differentiable function in the interval (0,2) then the value of int_(0)^(2)f(x) is

If f(x) and g(f) are two differentiable functions and g(x)!=0, then show trht (f(x))/(g(x)) is also differentiable (d)/(dx){(f(x))/(g(x))}=(g(x)(d)/(pi){f(x)}-g(x)(d)/(x){g(x)})/([g(x)]^(2))

RESONANCE-APPLICATION OF DERIVATIVES-Exersise-2 Part III
  1. If f(x) = 2x + cot^(-1) x + log ( sqrt(1+x^2 )-x) then f(x)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Which of the following statements are true :

    Text Solution

    |

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

    Text Solution

    |

  19. which of the following inequalities are valid-

    Text Solution

    |

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

    Text Solution

    |