Thread: question about finding maximum and minimum values

Hi, im stuck on a problem where the first derivative of a function is given and am asked to find the critical points and tell weather each is a maximum f minimum. I have no probem finding the critical points but dont you have to plug those back into the original function? Is there a way to go backwards from first derivative to the original function or am i missing something?
thank you

Originally Posted by cowboys111

Hi, im stuck on a problem where the first derivative of a function is given and am asked to find the critical points and tell weather each is a maximum f minimum. I have no probem finding the critical points but dont you have to plug those back into the original function? Is there a way to go backwards from first derivative to the original function or am i missing something?
thank you

find the second derivative and then plug in the critical points into it. if you get a negative answer, then the critical point is a local maximum, if you get a positive answer, then it's a local minimum, if you get zero, then it is a possible inflection point, further tests are needed, but let's cross that bridge if we get to it.

EDIT: This is my 5th post!!!!

Originally Posted by cowboys111

Hi, im stuck on a problem where the first derivative of a function is given and am asked to find the critical points and tell weather each is a maximum f minimum. I have no probem finding the critical points but dont you have to plug those back into the original function? Is there a way to go backwards from first derivative to the original function

The answer to that is yes.
But there is no need to do that. If the derivative is negative just to the left of the point and positive just to the right then the point is a minimum and visa versa for a maximum. If it has the same sign look for a point of inflection.

awesome it worked! thank you for your help