increasing and decreasing functions relative extrema

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 o..

(1) Let the given function be f (x) on the real number line R. (2) Differentiate the function f(x) with respect to x and equate it to zero i.e., put f '(x) = 0. Solve for x. These values of x which satisfy f '(x) = 0 are called Critical values of the function (3) Arra..

Introduction - The study of world of life is as old as man itself. All living organisms are made up of a few elements which are repeated in each of them. The basic unit of life - cell, is a structural and functional entity of life. Of all the environmental factors that affect plant life, ..

Atomic Number (Z) is the number of protons in the nucleus of an atom. It is also equal to the number of electrons since the atom is electrically neutral. Mass Number (A) is the total number of neutrons and protons present in the nucleus of an atom. The periodic law given earlier is now modifie..

1. Peptide hormones Insulin has a profound influence or carbohydrate metabolism. It facilitates entry of glucose and other sugars into the cells by increasing penetration of cell membranes and augmenting phosphorylation of glucose. This decreases glucose concentration in blood ..

>We see that as x increases, the value of e x also increases indefinitely. Also, as x decreases, the value of e x tends toward zero. The function e x is one-o..

For every game the team won, they earned points. The graph shows points earned for games won. Which sentence describes how the number of points relates to the number of games won? => The number of points increases as the number of games won increases. or The number of ..

Which of the following statement(s) is/are true for the graph of the function f ( x ) = x sin x in the interval [- π, π]? I. x - intercepts are (0, 0), (- π, 0) and (π, 0). II. The graph is decreasing in (- π, 0). III. y - intercept is (0, 0). IV. The graph is ..

' decreases and reaches minimum value. If the angle of incidence is further increased, the angle of deviation is increased. Let d m be the angle of minimum deviation. The refracted ray in the prism in that case will be parallel to the base. For minimum de..

The table shows the maximum pulse rate for people of different age, during aerobic activities. Age (years) 20 30 40 50 Pulse rate (beats/min) 175 166 157 148 Choose the relation that best represents the table. => The pulse rate doubles with age. or The pulse rate decreases with ..