derivatives of functions

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. We c..

This section explains how derivative can be used to check whether a function is increasing, decreasing or neither increasing nor decreasing in its domain. Let f be a function defined on an interval I and let x 1 and x 2 be any two points on I. (i) f is said to be incre..

Definition - The functional group is an atom, or a group of atoms which can replace one or more hydrogen/s in a hydrocarbon. This group when present in organic compounds defines the characteristic physical and chemical properties of that particular family of organic compounds. Thus a ..

Consider a continuous and derivable function f ( x ) with the following: f (-1) = 0 f (0) = 1 f (3) = 0 f ( x ) is maximum at x = 0 Which of the following would be the graph of f ′ ( x )? => Graph A or Graph B or Graph C or Graph D..

Which of the following is the derivative of the function f ( x ) = 1 4 coth ( x 4 ) - 1 12 coth 3 ( x 4 )? => - 1 16 cosech 4 ( x 4 ) or cosech 2 ( x 4 ) + 1 4 cosech 4 ( x 4 ) or 1 4 cosech 2 ( x 4 ) + 1 1 6 cosech 4 ( x 4 ) or - 1 4 cosech 4 ( x 4 ) ..

This chapter contains oxygen compounds in which oxygen is bonded to a carbon atom through a double bond. The functional unit >C = O, present in these compounds is called carbonyl group. We limit our study now to compounds having an acyl group (R - C = O) is bonded to hydrogen, ca..

The graph of a continuous and twice differentiable function f ( x ) is shown . Which of the following can be the graph of its first derivative f ′ ( x )? => Graph A or Graph B or Graph C or Graph D..

Which of the following is correct for a function that is differentiable at a point x = 3 ? => left hand side derivative = right hand side derivative at x = 3 or left hand side derivative may not be equal to the right hand side derivative at x = 3 or..

In this chapter, 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.In this chapter, we have studied various techniques of differentiation. Also,..

Integration and differentiation are a pair of inverse operations. So far, from a given function, we have been finding its derivative but the question arises: what is the function whose derivative is known? If the derivative of a functionh..