Home
Class 12
MATHS
Let h(x) =f(x)-a(f(x))^(3) for every rea...

Let `h(x) =f(x)-a(f(x))^(3)` for every real number x
h(x) increase as f(x) increses for all real values of x if

A

`a in (0,3)`

B

`a in (-2,2)`

C

`[3,oo)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
4
h(x) increases as f(x) decreases for all values of x if
`3a(f(x))^(2)-2 af(x)+le for all x in R`
or `33a lt 0 and 4a^(2)-12ale 0`
or `a lt 0 and a in [0,3]`
So , such a is possible
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|14 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Linked comprehension Type|2 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real number xdot Then (a) h is increasing whenever f is increasing (b) h is increasing whenever f is decreasing (c) h is decreasing whenever f is decreasing (d) nothing can be said in general

If f(x)=2 for all real numbers x, then f(x+2)=

Let f(x)=x-[x], for ever real number x ,w h e r e[x] is the greatest integer less than or equal to xdot Then, evaluate int_(-1)^1f(x)dx .

Let h(x) = min {x, x^2} , for every real number of X. Then (A) h is continuous for all x (B) h is differentiable for all x (C) h^'(x) = 1, for all x > 1 (D) h is not differentiable at two values of x

For all real numbers x , f(2x) = x^(2) - x + 3 . An expression for f(x) in terms of x is

Let f(x) = x-[x] , for every real number x, where [x] is integral part of x. Then int_(-1) ^1 f(x) dx is

If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

Let f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x) for some real number k. Determine(a) all real numbers k for which f(x) is constant for all values of x.

Let f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x) for some real number k. Determine(a) all real numbers k for which f(x) is constant for all values of x.

If f(x) is a function f:R-> R , we say f(x) has property I. If f(f(x)) =x for all real numbers x. II. f(-f(x))=-x for all real numbers x. How many linear functions, have both property I and Il ?

CENGAGE ENGLISH-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Linked comprehension type
  1. If H (x(0))=0 for some x=x(0)and (d)/(dx)H(x)gt2cxH(x) for all xgex(0)...

    Text Solution

    |

  2. Let h(x) =f(x)-a(f(x))^(3) for every real number x h(x) increase as ...

    Text Solution

    |

  3. Let h(x) =f(x)-a(f(x))^(3) for every real number x h(x) increase as ...

    Text Solution

    |

  4. If f(x) is strictly increasing function then h(x) is non monotonic fun...

    Text Solution

    |

  5. Let f(x)=x^(3)-9x^(2)+24x+c=0 have three real and distinct roots alpha...

    Text Solution

    |

  6. Let f(x)=x^(3)-9x^(2)+24x+c=0 have three real and distinct roots alpha...

    Text Solution

    |

  7. Let f(x)=x^(3)-9x^(2)+24x+c=0 have three real and distinct roots alpha...

    Text Solution

    |

  8. consider the graph of y=g(x)=f'(x) given that f(c ) =0, where y=f(x) i...

    Text Solution

    |

  9. Consider the graph of y=g(x)=f'(x) given that f(c) =0, where y=f(x) is...

    Text Solution

    |

  10. consider the graph of y=g(x)=f'(x) given that f(c ) =0, where y=f(x) i...

    Text Solution

    |

  11. consider the graph of y=g(x)=f'(x) given that f(c ) =0, where y=f(x) i...

    Text Solution

    |

  12. consider the graph of y=g(x)=f'(x) given that f(c ) =0, where y=f(x) i...

    Text Solution

    |

  13. Let f(x) = 4x^(2)-4ax+a^(2)-2a+2 and the golbal minimum value of f(x) ...

    Text Solution

    |

  14. Let f(x) = 4x^(2)-4ax+a^(2)-2a+2 and the golbal minimum value of f(x) ...

    Text Solution

    |

  15. Let f(x) = 4x^(2)-4ax+a^(2)-2a+2 and the golbal minimum value of f(x) ...

    Text Solution

    |

  16. Let f(x) =x^(3)-3(7-a)X^(2)-3(9-a^(2))x+2 The values of parameter a ...

    Text Solution

    |

  17. Let f(x) =x^(3)-3(7-a)X^(2)-3(9-a^(2))x+2 The values of parameter a ...

    Text Solution

    |

  18. Let f(x) =x^(3)-3(7-a)x^(2)-3(9-a^(2))x+2 The values of parameter a ...

    Text Solution

    |

  19. consider the function f(x) =1(1+(1)/(x))^(x) The domain of f(x) is

    Text Solution

    |

  20. consider the function f(x) =1(1+(1)/(x))^(x) The domain of f(x) is

    Text Solution

    |