Determining absolute extreme of function

f(x)=x^{2}+2x-4 Interval is [-1, 1]

What I did:

f'(x)=2x+2

x=-1

Plugged in:

One of my minimums is (-1, 0)

I'm confused on how to get the maximum now.

I did 0=x^{2}+2x-4

4=x(x+2)

4/(x+2)=x

But I don't think this is correct.

Please explain.

Thanks!

Re: Determining absolute extreme of function

Global maxima and minima can occur either at stationary points or at endpoints of the function. You have found the stationary point. Now evaluate each of the endpoints and see which of the three values is the largest and which is the smallest.

Re: Determining absolute extreme of function

Quote:

Originally Posted by

**Prove It** Global maxima and minima can occur either at stationary points or at endpoints of the function. You have found the stationary point. Now evaluate each of the endpoints and see which of the three values is the largest and which is the smallest.

Ok still kind of confused, like for example, if I had -x^2 + 3x and the Intervals are [0,3]

What I did was find the derivative which is -2x + 3, and so x=3/2

I plugged that back into the original equation, so the maximum is ((3/2),(9/4))

The minimums are (0,0) and (3,0), but I'm a bit confused how they got to the minimum

Just like with this problem as well.

I kind of need help, so a little more advice would be nice :)

Thanks!

Re: Determining absolute extreme of function

Like ProveIt said, you need to look at the points where the derivative is zero and ALSO the endpoints. You got a maximum where the derivative is zero, and the minima come from the endpoints.

- Hollywood