Home
Class 12
MATHS
If f is a real function such that f(x) >...

If `f` is a real function such that `f(x) > 0,f^(prime)(x)` is continuous for all real `x` and `a xf^(prime)(x)geq2sqrt(f(x))-2af(x),(a x!=2),` show that `sqrt(f(x))geq(sqrt(f(1)))/x ,xgeq1`.

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

If f is a real-valued differentiable function such that f(x) f'(x)lt0 for all real x, then

If f is a real-valued differentiable function such that f(x)f'(x)lt0 for all real x, then -

If f is a real- valued differentiable function such that f(x)f'(x) lt 0 for all real x, then

f(x) is real valued function such that 2f(x) + 3f(-x) = 15 - 4x for all x in R . Then f(2) =

If f is a function such that f(0)=2, f(1)=3 and f(x+2)=2f(x)-f(x+1) for every real x then f (5) is

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0) = 1 and f"(0) does not exist. Let g(x) = xf'(x). Then

If f(x+y)=f(x)+f(y) for all real x and y, show that f(x)=xf(1) .

If f(x)=xtan^(-1)x , find f^(prime)(sqrt(3)) .

If f(x)=xtan^(-1)x , find f^(prime)(sqrt(5)) .

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0)=1 and f''(0) does not exist. Let g(x) = xf'(x). Then

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let f(x)=(x^3-6x^2+12 x-8)e^xdot Statement 1: f(x) is neither maximum...

    Text Solution

    |

  2. Statement 1: The function f(x)=x^4-8x^3+22 x^2-24 x+21 is decreasing f...

    Text Solution

    |

  3. If f is a real function such that f(x) > 0,f^(prime)(x) is continuous ...

    Text Solution

    |

  4. Let f(x)=x^3-3x^2+6AAx in \mathbb{R} and g(x)={m a x :f(t ; x+1lt=tlt=...

    Text Solution

    |

  5. From a fixed point A on the circumference of a circle of radius r , th...

    Text Solution

    |

  6. The lower corner of a leaf in a book is folded over so as to reach the...

    Text Solution

    |

  7. h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4) where f''(x)> 0 AA x in (-3,4)...

    Text Solution

    |

  8. If 0<x1<x2<x3<pi, then prove that sin((x1+x2+x3)/3)>(sinx1+sinx2+sinx3...

    Text Solution

    |

  9. Prove: sin^2θ+cos^2θ=1

    Text Solution

    |

  10. Prove that (tan^(-1) 1/e)^2+(2e)/ sqrt(e^2+1)<(tan^(-1)e)^2+2/(sqrt(e^...

    Text Solution

    |

  11. If f(x)=x^3+bx^2+cx+d and 0ltb^2ltc then in (-oo,oo)

    Text Solution

    |

  12. The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x ...

    Text Solution

    |

  13. Find the values of x where f(x)=sin(lnx)-cos(lnx) in strictly increasi...

    Text Solution

    |

  14. Let f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...

    Text Solution

    |

  15. Find the possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is mon...

    Text Solution

    |

  16. Prove that for any two numbers x1 and x2.(2e^(x1)+e^(x2))/3gte^((2(x1)...

    Text Solution

    |

  17. Assertion Consider the following statements in SandR S: Both sinx and...

    Text Solution

    |

  18. Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f decreases in the interval

    Text Solution

    |

  19. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  20. Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sint...

    Text Solution

    |