Differentials Calculus

Differentials Calculus in mathematics is a part of calculus which has many important uses and can be used to derive quantities like change of rate, slope of a tangent at any point on the curve, maximum and minimum values of function etc. For instance, suppose we are given a continuous function whose slope, critical point and max or min values are to be calculated, we use application of differentiation. The first differential is used for the purpose of finding the rate change and the critical points whereas on differentiating the 1st differential again we get the max & min values.

Let us consider an example of differential calculus as follows: Suppose we have a function h (x) = 5 x⁵, then its first derivative would give us h’ (x) = 25 x⁴. Substituting h’ (x) = 0 we get x = 0. Thus the critical point is obtained at x = 0. In case the h’ (x) would have resulted in a fixed value; we say that there exist no min or max values for the function. In our example we are not getting any fixed value. Next we differentiate the 1st derivative again to get the maximum or minimum values. If the h’’ (x) comes – ve, then it is maximum value and for h’’ (x) + ve we get minimum value. In case h’’ (x) = 0 the value resembles an inflection point, and can be mistreated. In our example we would get h’’ (x) = 100 x3. Next we find out the maximum or the minimum value for the function.

Next we study how to add fractions with unlike denominators: It is a very simple concept and for solving such problems we take the LCM of the denominators. For instance: 12 /13 + 11 /10 = (120 + 143)/130 = 263/130. These concepts are important and are discussed in the icse sample papers in  detail. In the next session we will discuss about combination formula.