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Stetson University

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Problem 18

$15-22=$ Sketch the graph of $f$ by hand and use your sketch to

find the absolute and local maximum and minimum values of $f .$

(Use the graphs and transformations of Sections $1.2 . )$

$$f(t)=\cos t, \quad-3 \pi / 2 \leqslant t \leqslant 3 \pi / 2$$

Answer

abs $\&$ local min: $f(-\pi)=-1, f(\pi)=-1 \quad$ abs $\&$ local max: $f(0)=1$

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## Discussion

## Video Transcript

Okay, so tryingto graft the function f of t is equal to co sign t where t must be great angle to negative three pi over two, but is less than or equal to three pi over two Photographed a something. You understand how coastline works with within the unit circle when co sign is coastline of t is equal to zero or when you have a co signer zero I should say gonna have that our effort. Easy, quick, Troy, when you have a co signer pirate too. Effort is going equal to zero. When we have co sign off pie effort, he's gonna equal to negative one and have three Piper to f t is gonna be equal to zero once again. So let's try and map this out. So we have zero part 20 hi negatively three prior to zero And then the same thing applies for the negative values and negative pirate too is gonna equal to pi to secret deserve negative pies. Equal pirates is equal to zero. Same for I'm sorry. Negative pilot which is equal to negative lawyer and a key part two is zero. So the guard, basically they look something like this. All right, so it's Ah, it's just make your weight. So we need to find the local men's and Max for this We're gonna have actually, in this case is we have this small interval we're gonna have in absolute max. Ah, is there one? And then we're gonna have to look gas and local max minimums. Ah, pride negative way, You know, so negative by a little.

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