Author Topic: Local Maximum/Minimums Trig Addition of Ordinates (Read 762 times) Tweet Share

wildareal · « **on:** July 04, 2010, 10:29:00 pm »

Hi There,

f(x)=2cosx+2sinxcosx

find the local maximum and minimum values of f(x) for each of the following and state the corresponding x-value of each.

tram · « **Reply #1 on:** July 04, 2010, 10:33:31 pm »

take out 2cos(x) and use product rule

moekamo · « **Reply #2 on:** July 05, 2010, 01:52:45 am »

$f'(x) = -2\sin x + 2(\sin x \cdot -\sin x + \cos x \cdot \cos x) = -2\sin x + 2(\cos ^2 x - \sin ^2 x)$

so for max/min, $0=2\cos ^2x - 2\sin ^2x - 2\sin x \implies 0 = \cos ^2x - \sin ^2x - \sin x = 1- \sin ^2x - \sin ^2x -\sin x \implies 0 = 2\sin ^2x + \sin x - 1$

substitute, $a= \sin x \implies 0 = 2a^2+a-1 = (2a-1)(a+1) \implies \sin x = \frac{1}{2} \mbox{ or } -1$

solve this for x within domain if there is one, then sub back in f(x) for the max and min values

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Author Topic: Local Maximum/Minimums Trig Addition of Ordinates (Read 762 times) Tweet Share

wildareal

Local Maximum/Minimums Trig Addition of Ordinates

tram

Re: Local Maximum/Minimums Trig Addition of Ordinates

moekamo

Re: Local Maximum/Minimums Trig Addition of Ordinates

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