Home
Class 12
MATHS
If f : [ 5, 5] Ris a differentiable func...

If `f : [ 5, 5] R`is a differentiable function and if `f^(prime)(x)`does not vanish anywhere, then prove that `f( 5)f(5)`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Exercise 5.1|11 Videos
  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Exercise 5.2|6 Videos
  • 3D COORDINATION SYSTEM

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

    CENGAGE|Exercise Solved Examples And Exercises|137 Videos

Similar Questions

Explore conceptually related problems

If f:[-5,5]rarr R is differentiable function and iff'(x) does not vanish anywhere,then prove that f(-5)!=f(5)

If fquad :quad [quad -5,quad 5]rArr R is a differentiable function and if f'(x) does not vanish anywhere,then prove that f(-5)!=f(5)

If f:[-5,5]rarr R is differentiable and if f'(x) doesnt vanish anywhere,then prove that f(-5)!=f(5)

If f(x) is a twice differentiable function and given that f(1)=2,f(2)=5 and f(3)=10 then

If the function f defined on R-{0} os a dIfferentiable function and f(x^3)=x^5 for all x, then f'(27)=

If F:R rarr R given by f(x)=x^(3)+5 is an invertible function,than f^(-1)(x) is

If f(x) is an identity function, then f(5) is equal to

If f is continuously differentiable function then int_(0)^(1.5) [x^2] f'(x) dx is

If f is continuously differentiable function then int_(0)^(2.5) [x^2] f'(x) dx is equal to

Let f be a differentiable function defined on R such that f(0) = -3 . If f'(x) le 5 for all x then

CENGAGE-APPLICATION OF DERIVATIVES-Solved Examples And Exercises
  1. If f : [ 5, 5] Ris a differentiable function and if f^(prime)(x)does ...

    Text Solution

    |

  2. The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0

    Text Solution

    |

  3. Find the angle of intersection of y=a^xa n dy=b^x

    Text Solution

    |

  4. If the sub-normal at any point on y=a^(1-n)x^n is of constant length,...

    Text Solution

    |

  5. Find the cosine of the angle of intersection of curves f(x)=2^x(log)e ...

    Text Solution

    |

  6. Find the value of a if the curves (x^2)/(a^2)+(y^2)/4=1a n dy^3=16 x c...

    Text Solution

    |

  7. The acute angle between the curves y= |x^2 -1| and y=|x^2- 3| at their...

    Text Solution

    |

  8. In the curve x^(m+n)=a^(m-n)y^(2n) , prove that the m t h power of the...

    Text Solution

    |

  9. Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point ...

    Text Solution

    |

  10. For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent ...

    Text Solution

    |

  11. For the curve y=f(x) prove that (lenght n or mal)^2/(lenght or tanght...

    Text Solution

    |

  12. Find the condition if the equation 3x^2+4a x+b=0 has at least one root...

    Text Solution

    |

  13. Find c of Lagranges mean value theorem for the function f(x)=3x^2+5x+7...

    Text Solution

    |

  14. Let 0<a<b<pi/2dotIff(x)=|tanxtanatanbsinxsinasinbcosxcosacosb|,t h e n...

    Text Solution

    |

  15. Let f(x)a n dg(x) be differentiable for 0lt=xlt=2 such that f(0)=2,g(0...

    Text Solution

    |

  16. Prove that if 2a0 2<15 a , all roots of x^5-a0x^4+3a x^3+b x^2+c x+d=0...

    Text Solution

    |

  17. If f(x) is continuous in [a , b] and differentiable in (a,b), then pro...

    Text Solution

    |

  18. Prove that |tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot

    Text Solution

    |

  19. Using Lagranges mean value theorem, prove that (b-a)/bltlog(b/a)lt(b-a...

    Text Solution

    |

  20. If a &gt; b &gt;0, with the aid of Lagranges mean value theorem, prov...

    Text Solution

    |

  21. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

    Text Solution

    |