Application Of Derivatives

For all

Let then at x = 0, f has

If , then f (x) is

Let and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

In [0, 1] Lagranges Mean Value theorem is NOT applicable to

f(x) is cubic polynomial with f(2) = 18 and f(1) = -1. Also f(x) has local maxima at x = -1 and f '(x) has local minima at x = 0, then

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is , the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are

If '' > 0

If is a differentiable function such that for all , and , then