Home
Class 12
MATHS
If f : [-5, 5] to R is a differentiable ...

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

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise ILLUSTRATION|2 Videos
  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise SOLVED EXAMPLES|1 Videos
  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise JEE Previous Year|9 Videos
  • 3D COORDINATION SYSTEM

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

    CENGAGE|Exercise Solved Examples And Exercises|17 Videos

Similar Questions

Explore conceptually related problems

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2. f(1)=1, then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

If f is a real valued function such that f(x+y) = f(x) + f(y) and f(1)=5, then the value of f(100) is

If f (x) = (x + 1)/(x - 1) is a real function , x ne 1 , then f [f(2)] is . . . .

If f(x)=2x^(2)+3x-5 , then prove that f'(0)+3f'(-1)=0

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x)

Let f: (-5,5) rarr R be a differentiable function with f(4) = 1, f^(')(4) = 1, f(0) = -1 and f^(')(0) = 1 , If g(x) = f(2f^(2)(x)+2))^(2) , then - g^(')(0) equals

If f is the greatest integer function and g is the modulus function, then find the value of (g0f)(-5/3)-(fog)(-5/3)dot

CENGAGE-APPLICATION OF DERIVATIVES-Examples
  1. Let f(x) be differentiable function and g(x) be twice differentiable f...

    Text Solution

    |

  2. Let f(x) be differentiable function and g(x) be twice differentiable f...

    Text Solution

    |

  3. If f : [-5, 5] to R is a differentiable function function and if f'(x)...

    Text Solution

    |

  4. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

    Text Solution

    |

  5. Let f:[2,7]vec[0,oo) be a continuous and differentiable function. Then...

    Text Solution

    |

  6. Let f(x)a n dg(x) be differentiable function in (a , b), continuous at...

    Text Solution

    |

  7. Using Lagranges mean value theorem, prove that |cosa-cosb|<|a-b|dot

    Text Solution

    |

  8. Let f(x)a n dg(x) be two differentiable functions in Ra n df(2)=8,g(2)...

    Text Solution

    |

  9. Suppose alpha,betaa n dtheta are angles satisfying 0<alpha<theta<bet...

    Text Solution

    |

  10. Let f be continuous on [a , b],a >0,a n d differentiable on (a , b)dot...

    Text Solution

    |

  11. Prove that the equation of the normal to x^(2/3)+y^(2/3)=a^(2/3) is yc...

    Text Solution

    |

  12. If the area of the triangle included between the axes and any tangent ...

    Text Solution

    |

  13. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

    Text Solution

    |

  14. If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve aga...

    Text Solution

    |

  15. Find the condition for the line y=m x to cut at right angles the conic...

    Text Solution

    |

  16. If the curves ax^(2) + by^(2) =1 and a(1) x^(2) + b(1) y^(2) = 1 inte...

    Text Solution

    |

  17. A man is moving away from a tower 41.6 m high at the rate of 2 m/sec. ...

    Text Solution

    |

  18. If f is continuous and differentiable function and f(0)=1,f(1)=2, then...

    Text Solution

    |

  19. Let a , b , c be three real numbers such that a<b<cdotf(x) is continuo...

    Text Solution

    |

  20. Use the mean value theorem to prove e^xgeq1+xAAx in R

    Text Solution

    |