I need help finding out the biggest and smallest values of;

f(x)=2(cosx)^2 - 2sinx + 1

without using the derivative.

Please, need help as soon as possible!

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- Feb 7th 2008, 08:21 AMweasley74[SOLVED] Help! - Values
I need help finding out the biggest and smallest values of;

f(x)=2(cosx)^2 - 2sinx + 1

without using the derivative.

Please, need help as soon as possible! - Feb 7th 2008, 08:25 AMcolby2152
- Feb 7th 2008, 08:37 AMweasley74
what about the smallest value..? is that just the other way around?

- Feb 7th 2008, 09:03 AMcolby2152
- Feb 7th 2008, 11:40 AMweasley74
so for minimum x=pi/2 +2npi

and for maximum x=0, x=pi+2npi ? - Feb 7th 2008, 04:17 PMSoroban
Hello, weasley74!

Quote:

Find the biggest and smallest values of: .

without using the derivative.

We have: .

Let

This is a down-opening parabola; its maximum is at its vertex.

. . The vertex is at: .

Hence, the maximum is: .

Normally, there is no minimum for this parabola.

. . However, the values of are limited: .

The minimum occurs at an endpoint of the interval.

. . And we find that the minimum is: .

- Feb 7th 2008, 11:24 PMweasley74
- Feb 8th 2008, 02:31 AMmr fantastic
Are you familiar with parabolas? Do you know how to find the turning point of a parabola?

There are many ways to get the turning point - Soroban gave one which clearly you're not familiar with. What about completing the square to get turning point form? You've gotta have met that one ....?

.

Maximum turning point at , that is, f(u) has a maximum value of (corresponding to .....) - Feb 8th 2008, 02:39 AMmr fantastic
- Feb 8th 2008, 04:36 AMcolby2152
- Feb 8th 2008, 05:48 AMKrizalid

May be this could be another way to get minimum point.