I need an example or more of optimation problems - finding maximum values.

Thanks

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- May 23rd 2010, 01:36 PMlorica2000Optimization Problems
I need an example or more of optimation problems - finding maximum values.

Thanks - May 23rd 2010, 03:37 PMSpringFan25
wow, choose your own question :D

I'll make an easy one then.

Find the maximum of

Firstly, this is a familiar graph (upside down parabola, shifted around). The maximum value of y will be 15, occuring at x=1.

Now, to prove it:

**Step 1: Find the derivative of the function you want to maximuse**

**Step 2: Set the derivative to zero to find x:**

**Step 3: Find the value of y that corresponds to this value of x**

**Step 4:Check you have a maximum**You can do this by checking the y values on either side are less than 15, or by checking that the second derivative is negative

**Explanation**

We found the maximum by looking for the point where the gradient was 0. This is the point where the curve stops increasing/decreasing, so it will be a maximum or a minimum.