Solving Applied Optimization Problems with Differential Equations

There are many different rules for mathematics field. Among them, solving the problems with differential equations which there are first derivative test and second derivative test. There were use to solve the problem of practical life such as profit and loss of the business system, maximum and minimum of the dimensions and increasing and decreasing of the function domain. In this paper, we use derivatives to find the extreme values of functions, to determine and analyze the shapes of graphs and to find numerically where a function equals zero. Rolle's Theorem and its examples are expressed. The first derivative test to determine where the differential equation increases and decreases is given. Similarly, the second derivative test to determine. Variety of optimization problems are solved by using derivatives. The dimension of various shape with fixed perimeter having maximum area are computed. The dimension for the least expensive cylindrical can of a given volume are computed.