Rules that Govern Constant Function

The basic rule

In the case of polynomials and rational functions, the building blocks are the functions f(x)=c and g(x)=xn, where n is a positive integer. These are the building blocks from which all polynomials and rational functions are constructed. For the purpose of effectively determining the derivatives of polynomials and rational functions without having to resort to the limit definition of the derivative, it is necessary to first create formulas for differentiating these fundamental functions.

The Constant Rule 

It is necessary to first apply the limit definition of the derivative to the constant function f(x)=c to obtain the derivative of the function. Due to the fact that both f(x) and f(x+h) are equal to c for this function, we gain the following result:

f'(x) = lim    f(x+h)- f(x)

          h→0     _________

                        h

      =  lim        c –  c

          h→0   ______

                         h

      =  lim     0

          h→0       __

                    h

      = lim   0=0

         h→0     

The constant rule is the term used to describe the rule for differentiating constant functions. A constant function has a derivative equal to zero; that is, because a constant function is a horizontal line, the slope of a constant function, or the rate at which it changes, equals 0. 

Constant function

A constant function is a function that has the same range for all possible values of the domain parameter. A constant function is represented graphically by a straight line that is parallel to the x-axis. With reference to the x-axis, the domain of the function is represented by the x-value, and the range of the function is represented by the letter y or f(x), which is noted with reference to the y-axis. 

It is possible to think of any function in terms of a constant function when it has the form y = K, where K is a constant and K might be any real number. It can alternatively be expressed as f(x) = k. It is important to notice at this point that the value of f(x) will always be ‘k,’ and that this value is independent of the value of x. In general, we can define a constant function as a function that always has the same constant value, regardless of the value of the input data that it receives.

 Constant functions can be illustrated by the following examples:

f(x) = 0

f(x) = 1

f(x) = π

f(x) = 3

f(x) = −0.3412454

f(x) equal to any other real number that comes to mind

When dealing with constant functions, one of the most exciting aspects is that we may use whatever real number we want for x and we will instantly know the value of the function at that x without having to perform any calculations.

 Conclusion

The constant rule is the term used to describe the rule for differentiating constant functions. A constant function has a derivative equal to zero; that is, because a constant function is a horizontal line, the slope of a constant function, or the rate at which it changes, equals 0.A constant function is a function that has the same range for all possible values of the domain parameter. A constant function is represented graphically by a straight line that is parallel to the x-axis. With reference to the x-axis, the domain of the function is represented by the x-value, and the range of the function is represented by the letter y or f(x), which is noted with reference to the y-axis.In the case of polynomials and rational functions, the building blocks are the functions f(x)=c and g(x)=xn, where n is a positive integer. These are the building blocks from which all polynomials and rational functions are constructed.