AP Calculus AB

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Calculus is a very important section of Mathematics which involves the study of the rate of change of

functions and their areas. The two important topics of Calculus are Differentiation and Integration (also

known as Anti differentiation). These two topics contain different techniques of solving various functions

based on them. AP calculus AB is the Advanced placement exam given for high school to test them in

Calculus.



Example 1:Find the derivative of the function, f(x) = 4x2 + 6x – 9


Power rule of the Derivatives: d f(xn)/dx = n*xn-1

Given function: 4x2 +6x - 9

Applying the above formula for every term of the function, we get

Derivative of the given function: d f(x)/dx= d(4x2)/dx + 6 *d(x)/dx – d(9)/dx

df(x)/dx = 4 * 2 * x2-1 + 6x – 0 (Derivative of a constant is always ‘0’)

df(x)/dx = 8x1+ 6

Hence the derivative of the function f(x) = 4x2 + 6x – 9 is 8x + 6


 
Example 2: Find the integral (or anti-derivative) of the function,f(x) = 8x + 6.


The Power Rule of Integration says that ∫ (x) n dx = x (n+1)/ (n+1) + c

where ‘c’ is a constant

Using the above formula we get,

∫ f(x) dx = 8 * x1+1/ (1+1) +6 * x0+1/ (0+1) + c

∫ f(x) dx = 8 * x2/ 2 + 6 * x1/ (1) + c

∫ f(x) dx = 4x2+6x + c

 
 
 

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