I dont know how to do this?

Question

Find the points at which y = f(x) = x10−6x has a global maximum and minimum on the interval 0 ≤ x ≤ 3.5.

I really need help with the global max

Thanks

Answer 1

By x10, do you mean x^10? (x to the 10th power) I assume that's what you mean.

To find the global min and max:
(1) Find relative extrema
(2) Test the endpoints

So, for (1), we set the derivative to 0:
10x^9 - 6 = 0
10x^9 = 6
x^9 = .6
x = (.6)^(1/9) whatever that is. If you know second derivative test, you can use that to show this is a min. Or, if you have a calculator, you can just plug it in to find f(x). Should be around -5.1.

That's the only critical point, so now we move on to step (2): testing endpoints.

When x=0, f(x)=0. Nice.
When x=3.5, f(x)=275833.7, roughly.

The highest number was 275833.7, so the global max happens there. (3.5, 275833.7).

The lowest number was -5.1, so the global min happens there. ( .6^(1/9), -5.4(.6)^(1/9) ).

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Um, this is for a calculus class, right?

Answer 2

This looks familiar but I dont know anything about "global max". Sorry.