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

1 Answer
May 7, 2018

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