Home
Class 12
MATHS
Let varphi(x)=f(x)+f(2a-x) and f"(x)>0 f...

Let `varphi(x)=f(x)+f(2a-x)` and `f"(x)>0` for all `x in [0,\ a]` . Then, `varphi(x)` (a) increases on `[0,\ a]` (b) decreases on `[0,\ a]` (c) increases on `[-a ,\ 0]` (d) decreases on `[a ,\ 2a]`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

  • INDEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|1443 Videos

Similar Questions

Explore conceptually related problems

If f(x)=xe^(x(x−1)) , then f(x) is (a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

If f(x)=x e^(x(x-1)) , then a) f(x) is increasing on [-1/2,1] b) decreasing on R c) increasing on R (d) decreasing on [-1/2,1]

Let g(x) = 2 f(x/2)+ f(2-x) and f''(x) lt 0 forall x in (0,2) . Then calculate the interval in which g(x) is increasing.

Let g(x)=2f(x/2)+f(2-x) and f''(x) < 0 AA x in (0,2). If g(x) increases in (a, b) and decreases in (c, d), then the value of a + b+c+d-2/3 is

If f''(x) le0 "for all" x in (a,b) then f'(x)=0

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)

If f'(x^2-4x+3)gt0 " for all " x in (2,3) then f(sinx) is increasing on

Let g(x)=f(x)+f(1-x) and f''(x)>0AAx in (0,1)dot Find the intervals of increase and decrease of g(x)dot

If the function f(x) increases in the interval (a , b),a n dvarphi(x) [f(x)]^2 , then varphi(x) increases in (a , b) varphi(x) decreases in (a , b) we cannot say that varphi(x) increases or decreases in (a , b)dot none of these

RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
  1. The function f(x)=x^2\ e^(-x) find the derivative with respect to x

    Text Solution

    |

  2. Function f(x)=cosx-2\ lambda\ x is monotonic decreasing when (a) lambd...

    Text Solution

    |

  3. In the interval (1,\ 2) , function f(x)=2|x-1|+3|x-2| is (a) monotonic...

    Text Solution

    |

  4. Function f(x)=x^3-27 x+5 is monotonically increasing when (a) x<-3 (b...

    Text Solution

    |

  5. Function f(x)=2x^3-9x^2+12 x+29 is monotonically decreasing when (a) x...

    Text Solution

    |

  6. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then (a) k<3 ...

    Text Solution

    |

  7. f(x)=2x-tan^(-1)x-log{x+sqrt(x^2+1)} is monotonically increasing when ...

    Text Solution

    |

  8. Function f(x)=|x|-|x-1| is monotonically increasing when (a) x<0 (b) ...

    Text Solution

    |

  9. Every invertible function is (a) monotonic function          (b) co...

    Text Solution

    |

  10. In the interval (1,\ 2) , function f(x)=2|x-1|+3|x-2| is (a) increasin...

    Text Solution

    |

  11. If the function f(x)=cos|x|-2a x+b increases along the entire number s...

    Text Solution

    |

  12. The function f(x)=x/(1+|x|) is (a) strictly increasing (b) strictly...

    Text Solution

    |

  13. The function f(x)=(lambdasinx+2cosx)/(sinx+cosx) is increasing, if (a)...

    Text Solution

    |

  14. Function f(x)=a^x is increasing on R , if (a) a >0 (b) a<0 (c) a<1 ...

    Text Solution

    |

  15. Function f(x)=(log)a x is increasing on R , if (a) a<0 (b) a >1 (c) ...

    Text Solution

    |

  16. Let varphi(x)=f(x)+f(2a-x) and f"(x)>0 for all x in [0,\ a] . Then, va...

    Text Solution

    |

  17. If the function f(x)=x^2-k x+5 is increasing on [2,\ 4] , then (a) k i...

    Text Solution

    |

  18. The function f(x)=-x//2+sinx defined on [-pi//3,\ pi//3] is (a) increa...

    Text Solution

    |

  19. If the function f(x)=x^3-9k\ x^2+27 x+30 is increasing on R , then (a)...

    Text Solution

    |

  20. The function f(x)=x^9+3x^7+64 is increasing on (a) R (b) (-oo,\ 0) (...

    Text Solution

    |