**The function ƒ is increasing before x =0**, and also it is** increasing after x=0** such a point of the function is **called the point of inflexion**. Point of inflexion derivative rule detail:

**NOTE:**

**(1) A stationary point is called turning if it either a maximum point or a minimum point.**

**(2) if ƒ’(x) >0 before the point x =a ,ƒ’(x) = 0 before the point x =a and ƒ’(x) >0 after x =a**

**then ƒ** does not have a r**elative maxima.**

See the graph of **ƒ(x) = x³** in this case we have

** ƒ’(x) =3x²**

** ƒ’(x)(0- ε) = 3(-ε)²= 3ε²>0**

and

**ƒ’(x)(0+ ε) = 3(ε)²= 3ε²>0**

which point has these two conditions is called the point** of inflexion.**

**Point of inflexion derivative rule:**

**What is the first Derivative rule:**

**Let ƒ** be a differentiable in neighborhood where **ƒ’(c)=0**

**Relative maxima of ƒ:**

**(1) if ƒ’(x)** changes **sign positive to negative as x** increases through c,** then ƒ(c)**is the** relative maxima of ƒ.**

**Relative minima of ƒ:**

**(2) if ƒ’(x) changes sign** from **negative to positive** as x increases through c, then if **ƒ’(c)** is** called the relative minima of ƒ.**

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