how to use the mean value theorem

Rolle's Theorem - Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..

Theorem 7: - Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b..

Which of the following functions satisfies the mean value theorem? => f ( x ) = x 2 - 6 , x ∈ [7, 8] or f ( x ) = log x , x ∈ [-7, 8] or f ( x ) = [ x ], x ∈ [-7, 7] or f ( x ) = | x |, x ∈ [-8, 8]..

Gauss' Theorem - We have already learnt to find the electric field intensity due to a charged conductor using Coulomb's law. Gauss' theorem can also be used to calculate the electric field intensity provided there is a symmetry in the charge distribution. Can..

Using Binomial theorem, prove that: ..

By trial and error method, find the factor of the constant for which the given expression becomes equal to zero. Divide the expression by the factor that is determined in step 1. Factorise the quotient. If the quotient is a trinomial, factorise it further. If the expression is a 4 t h ..

Since a velocity gradient exists across the tube, the mean velocity of the liquid is to be considered. The viscous drag which comes into play when the liquid is in motion, is not taken into account. In above conservation principle, part of K.E. is converted into heat..

Let f be a differentiable function on I and let x 0 be any interior point of I. Then (a) If f attains its absolute maximum value at x 0 , then f ' (x 0 )= 0 (b) If f attains its absolute minimum value at x 0 , then f '(x 0 ) = 0. In view of the above theorems, we sta..

If f(x) is a polynomial in x and is divided by x-a; the remainder is the value of f(x) at x = a i.e., Remainder = f(a..