Question

How do you find all critical point and determine the min, max and inflection given `V(w)=w^5-28`?

Answer 1

Use Your First and Second Derivative

Explanation:

I first like to start with taking my first and second derivatives:
`V'(w)=5w^4`
`V''(w)=20w^3`

The min and max are points where `V'(w)=0` so lets start with them.

`0=5w^4`
`0=w^4`
`0=w`

Now we test to see if `w=0` is a min, max, or none. We do this by using the second derivative. If our Final answer is greater than zero we know it's a minimum, if our final answer is less than zero we know it's a maximum and if our final answer is zero we know it's a turning point (think x^3 @ x=0).

`V''(0)=20(0)^3`
`V''(0)=0`

Since our answer is zero we know its a turning point.

This tells us that this equations has no Max or a Min. However, it does have a turning point at `w=0`