Calculus Concepts Assignment Example | Topics and Well Written Essays - 750 words

Calculus Concepts - Assignment Example For instance, a function y +3x +2 = 0 is expressed with both dependent and independent variables. Although implicit functions can be converted to explicit functions, it may result to a complex function which may be hard to solve. Implicit differentiation is useful in differentiating implicit functions (functions not in the form y = f(x)). Given a function say , implicit differentiation demands we differentiate all elements of the equation with respect to x, even y variables but not treating y as a constant. This would give: In the second education, all functions of y are differentiated using chain rule where . Once the differential is performed is made the subject of the formula. Implicit differentiation is useful in performing implicit functions. Instead of putting y the subject of the formula and making the function a complex one, implicit differentiation assists in simplifying implicit functions. Logarithmic functions are useful in solving differential problems that involve complex product or quotient rule. In logarithmic differentiation, the function is expressed in the form of the natural logarithm, and it is implicitly differentiated. Given a function with a lengthy product that would give a huge sum while using the product rule, logarithmic differentiation comes in handy. For instance; One of the applications of Calculus is in curve sketching. Curve sketching involves using specific values of functions to estimate its structure. In curve sketching, we have the absolute maximum and a local maximum. The main difference between the two is that the absolute maximum is the maximum value of the function that takes over the whole domain. This means that in a given range, the absolute maximum is the largest value of the function obtained by performing a differentiation of the functions and equating it to zero. On the other hand, the local maximum is the largest value of the functions on a given section but not on the entire domain. The given image below