## IB Maths SL Point of inflexion

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

### IB Maths SL Point of inflexion

IB Mathematics HL – Derivatives, 2nd derivative test and Points of inflection

How can we find if the function $f(x)=x^3-12x+2$ has a point of inflexion?

Thanks
Oliver

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Joined: Mon Jan 28, 2013 8:08 pm

### Re: IB Maths SL Point of inflexion

IB Mathematics SL – Derivatives, Points of inflexion

We know that

If $f''(x_{0})=0$ and the second derivative function changes sign around $x_{0}$ then at $x= x_{0}$ the function has a point of inflection.

The first derivative function is

$f'(x)=3x^2-12$

The second derivative function is

$f''(x)=6x$

By setting the second derivative equal to zero,

$f''(x)=6x=0 \Rightarrow x =0$
To determine the set of values for which the function is concave up or concave down we need to solve the following inequality

$f''(x)=6x>0 \Rightarrow x >0$

We observe that the function is concave up when $x >0$ and is concave down when $x <0$

Thus at $x =0$ the function has a point of inflexion which has coordinates (0,2).

Hope these help!!
miranda

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Joined: Mon Jan 28, 2013 8:03 pm

### Re: IB Maths SL Point of inflexion

thanks miranda
Oliver

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Joined: Mon Jan 28, 2013 8:08 pm