Thread: derivative function

Consider the function .

This function has an absolute minimum value equal to



and an absolute maximum value equal to

what have you done with this problem?

Absolute max or min is where first derivative is zero.






So absolute max or min can be at or . But to find out which one which you plug-in the values into the function and find out which one's larger than the other.

Now plug-in and separately into you'll find that
The function has absolute max at

And has absolute min at

You can check it in the following graph to be sure:

Originally Posted by x3bnm

Absolute max or min is where first derivative is zero.






So absolute max or min can be at or . But to find out which one which you plug-in the values into the function and find out which one's larger than the other.

Now plug-in and separately into you'll find that
The function has absolute max at

And has absolute min at

You can check it in the following graph to be sure:

It should be pointed out that in general, absolute maxima and minima could lie at turning points (where the first derivative is 0) OR at endpoints of the function.

Originally Posted by Prove It

It should be pointed out that in general, absolute maxima and minima could lie at turning points (where the first derivative is 0) OR at endpoints of the function.

Good point Prove It. Thanks for that.