Differentiation

Differentiation

 FUNCTION
Constant : A quantity, whose value remains unchanged during mathematical operations, is called a constant quantity. The integers, fractions,\( \pi \) , e, etc are all constants.

Variable: A quantity which can take up different value is called a variable. A variable is usually represented as x, y, z etc.

Function : A quantity y is called function of a variable x, if corresponding to any given value of x, there exists a single definite value of y. The phrase ‘y is a function of x’ is represented as y = f(x)
To illustrate, consider that y is function of the variable x as given by
    y = 3x² +7x +2
If x = 1, then y = 3(1)² + 7(1) + 2 = 12 and when x =2, y = 3 (2)² + 7(2) + 2= 28

Therefore, when the value of the variable x is changed, the value of the function y also changes but corresponding to the each value of x, we get a definite value of y. Hence, y = 3x² +7x + 2 represents a single-valued function of x.