Inflection Points

An Inflection Point is where a curve changes from Concave upward to Concave downward (or vice versa)

Determine Inflection Points

• If $f^{\prime \prime }(x)=0$ changes sign from positive to negative (or vice versa) at a particular $x$-value, that point could be an inflection point.

Example

Let's consider the function f(x)= x^3 − 3x.

• The first derivative is $y^{\prime }=3x^2-3$
• The second derivative is $y^{\prime \prime }=6x$

Next, we’ll set the second derivative equal to zero to find the Inflection Points: $6x=0$