Differential calculus functions6/20/2023 ![]() Quadratic approximation is the improvisation of the linear approximation. The rate of change and the instantaneous rate of change can be termed as their concepts.Īverage rate of change = f ( x h ) − f ( x ) ( x h ) − x =\frac f ′ ( c ) = b − a f ( b ) − f ( a ) ĭerivatives also gives the linear approximation of a function at a given point. Print based materials Rate of change the problem of the curve Instantaneous rate of change and the derivative function Shortcuts for differentiation (. The rate of change can be described by the gradient of a curve at a given point and this can be determined by using the concept derivative. The given function f(x) and its derivative f’(x) represent the rate of change of the given function. The rate of change is one of the most important applications of derivatives. ![]() In graphs it is easy to see at which rate the function is changing as the independent variable changes because the graphs give a visual representation of the function. It is very useful to determine how fast or at what rate the things are changing. In mathematics there are several ways to interpret the change in the things, for example for representing the changes we can use algebraic formulae or graphical representation. ![]() Here are the applications of the differential calculus. ![]() In the further section let’s see where we can use the differential calculus. In the above graph, a blue curve and a red line passing through the given black point is the tangent line. Geometrically, the slope of a tangent line to the graph of a given function is the derivative at a point. Differentiation is the process of finding the derivative of a given function. Differential calculus helps in study about the change in rate of a function, also finding the derivatives of a function. ![]()
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