What is calculus used for

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Calculus is the section in mathematics which is used in various fields and this branch of mathematics helps us analyze the behaviors of different functions. Calculus is a vast section and it includes various applications such as finding the area between the curves, maximum and minimum values possible for a function, structure of the graph and its continuity etc. These applications of calculus are used in different fields such as engineering and technology, business etc. and these concepts also help us find solutions to complex problems.
 
Example 1: Find the slope of the given straight line, f(x) = 2x + 11 using the derivative method.
In order to find the derivative, we can use the Power rule of the Derivatives:
èd(xn)/dx = n * xn-1
We can distribute the derivative to both the terms:
èd(2x + 11)/dx è[ d(2x)/ dx ] + [ d(11)/ dx ]
Using the above formula, we get
è2(x1-1) + 0 = 2
Hence the slope or the derivative of the given straight line is 2.
 

Example 2: Find the slope of the tangent drawn to the given function, f(x) = x2 + 3x at x = 1.
Using the Power rule of the Derivatives:
èd(xn)/dx = n * xn-1
èd(x2 + 3x)/dx è[ d(x2)/ dx ] + [ d(3x)/ dx ]
Using the above formula, we get
è2(x2-1) + 3(x1-1) = 2x + 3
Hence the slope is = 2x + 3.
When x = 1, the slope = 2(1) + 3 = 2+ 3 = 5
Hence the slope of the tangent to the curve at x = 1 is 5.

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