solve derivative as a function

x = a is called a point of inflexion. Rolle's theorem: If a function f(x) is such that (i) f (x) is continuous on [a,b] (ii) f (x) is differentiable on (a,b) and (iii) f (a) = f (b) Geometrical interpretation of Rolle's theorem Let AB be the graph of y = f(x) such that A = (a , f(a)) and ..

Let f be a differentiable function on an interval I and let a I. Let f "(a) be continuous at a. Then i) 'a' is a point of local maxima if f '(a) = 0 and f "(a) < 0 ii) 'a' is a point of local minima if f '(a) = 0 and f "(a) > 0 iii) The test fails if f '(a) = 0 and f "(a) = 0. In th..

The equation that involves one (or) more derivatives of some unknown functions which are required to be found is called => Non linear equation or Differential equation or Linear equation or Quadratic equation..

We have already defined, for a continuous function f(x) on a closed interval [a, b] as the area of the region bounded by the curve y = f(x), X-axis and x= a and x = b. In other words, area of the shaded region is a function of x. The function A(x) is shown in figure be..

We thus observe, without actually solving the quadratic equation (a) We can find the value of every symmetric function involving the roots of the equation in terms of the coefficients of the equation. (b) We can find a quadratic equation whose roots are any one of the following ..

Let f (x) be the real valued differentiable function..

Functions Limits and Continuity - 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 ..

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 con..

Increasing and Decreasing Functions - 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 b..

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 and insulin is commo..