Differentiable

Differentiable

We know that differentiable means Derivatives of function exists

Example:

x²+5x is it differentiable?

Derivative Rules

Derivative Rules shows that derivative of x2 is 2x and derivative of x is 1 so the derivative of whole

Function is 2x+5

Fact: Here, We can say that x²+5x is differentiable.

And, also it must exist for every value in function’s Domain

Domain: In its simplest form, the domain is all those values that we put into a function.

Example:

We say that its domain is real numbers

For x²+5x its derivative still exist for all real numbers

Fact: x²+5x is still differentiable

Example:

The function f(x)=|x| (absolute value function)

Recalling:

f(x)=|x| is called abs(absolute value function)

Graph:

|x| looks like in graph:

Fact: At (0,0) it makes an right angle

It is an even function!

Even function:

A function is known as even function when:

F(x)=f(-x)

Example:

F(x)=cosx

Domain: Its domain is real numbers.

Range: It consists of non negative real numbers