But, in reality it does have some meaning like that. We sometimes call the right-hand side of that equation the differential of f , but when we do we usually write dx instead of D x . The point of that is to approximate the function by the linearization , the differential .
Solution Let's say that the side of the cube is measured as x .
Find the linear approximation of sinx for x near 0. 4 Applications of differentiation 4.1 Maximum and Minimum Values. One of the primary applications of calculus is to optimization problems, finding how to configure a situation to result in the largest, or smallest, value of a particular output. Such things as finding the price of a product you are selling, to maximize the profit, or how to design a box to minimize the materials required to build it, are standard examples of optimization. From a theoretical point of view, this theorem shows that an optimization problem will always have a solution under the right circumstances.