derivatives of functions

We have studied various techniques of differentiation. Also, we have studied the method of obtaining higher order derivatives of functions which is useful in maxima and minima problems...

After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the p..

From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integratio..

Two indefinite integrals with the same derivative lead to the same family of curves and so they are equivalent. Comparison between differentiation and integration: 1. The derivative of a function, when it exists is a unique function. The int..

The concept of limits leads to define and describe continuity and derivative of the function. The continuity of a function has practical as well as theoretical importance. We plot graphs by taking the values generated in the laboratory or collected in the field. ..

1. f ' (a) exists at x = a iff Lf ' (a) = Rf ' (a). Where Rf '(a) is Right hand derivative and Lf '(a) is Left hand derivative. 2. Derivability implies continuity. 3. Derivative of a constant function is zer..

Introduction - During the course of study of Mathematics, we must have come across several parts of inverse operations like (addition, subtraction) (multiplication, division) (forming an equation whose roots are given - solving a given equation) and so on. In practical situations, we may be interes..

Let y = f (x). The derivative of f at x is denoted by f '(x). Finding the derivative of a function using the above definition is called differentiation from first principle..

Differentiability - We have already defined the derivative of a function f(x) at a particular point 'a' and derivative of f(x) in general for the variable x as f (a) and f (x) respectively. The restriction in both the cases is that 'the limit must exist'. IfWe have alr..

Find the local maxima or local minima, if any, for the following function using first derivative test f (x) = x 3 - 6x 2 + 9x +..