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#