# How do you find all critical point and determine the min, max and inflection given #f(x)=2x^3-x^2+1#?

##### 1 Answer

Jan 11, 2017

#### Explanation:

We can find the critical points by equating the first derivative to zero:

so the critical points are:

To determine if they are local extrema and to find inflection points we calculate the second derivative:

So we have a single inflection point at

Based on the sign of the second derivative we can also conclude that

graph{2x^3-x^2+1 [-0.3227, 0.9273, 0.7125, 1.3375]}