Home
Class 12
MATHS
Verify Mean Value Theorem, if f(x)=x^2-4...

Verify Mean Value Theorem, if `f(x)=x^2-4x-3` in the interval [a, b], where `a = 1 and b = 4`.

Text Solution

Verified by Experts

The given function is`f(x)=x^2-4x-3`
polynomial function is always a continuous function
Hence f(x) is a continuous function at [1,4]

` f ′ (x)=2x−4`

`Now f(1)=1^ 2 ...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|47 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.5|18 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.3|15 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

  • DETERMINANTS

    NCERT ENGLISH|Exercise All Questions|116 Videos

Similar Questions

Explore conceptually related problems

Verify Mean Value Theorem, if f(x)=x^3-5x^2-3x in the interval [a, b], where a = 1 and b = 3 . Find all c in (1, 3) for which f^(prime)(c)=0 .

Verify mean value theorem, if f(x) = x^(2) - 4x in the interval [1, 4].

Verify the Mean Value Theorm for f(x)= x^2 in the interval [2,4].

Verify Rolle's theorem for f(x)=sqrt(1-x^(2)) in the interval [-1,1].

Verify Rolles theorem for the function f(x)=(x-a)^m(x-b)^n on the interval [a , b], where m , n are positive integers.

Verify Rolles theorem for the function f(x)=x^2-5x+6 on the interval [2, 3].

Verify Lagrange's Mean Value Theorem for the function f(x)=sqrt(x^(2)-x) in the interval [1,4] .

Verify Rolles theorem for the function f(x)=x^2-5x+6 on the interval [2,3]dot

Verify Rolle's theorem for the function f(x) = x^(2) in the interval [-1,1] .

Verify Rolle's theorem for the function f(x) = cos2x in the interval [0, pi] .