Sketch the graph of f by hand and use your sketch to find...

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(t) = 6 cos(t), −3𝜋/2 ≤ t ≤ 3𝜋/2 absolute maximum value absolute minimum value local maximum value(s) local minimum value(s)

Transcript

00:01 All right, so they want us to graph this by hand.

00:04 You graph this function by hand and find the local maximum and minimum values.

00:09 Okay, so here's our function.

00:13 F of t is equal to six cosine of t.

00:23 All right.

00:24 So to graph this, if you think back to, you know, graphing these trig graphs, cosine and cosine, sine curve, cosine curves.

00:34 So it repeats every 2 pi.

00:37 So from 0 to 2 pi, you get it.

00:39 So here's what our graph looks like.

00:41 Here's our t -axis.

00:44 Here's zero right here.

00:48 Our amplitude is going to be 6.

00:50 So it's going to go up to 6 and down to negative 6.

00:55 You know, if we go out here to 2 -pi and we go back here to negative 2 -pi, we don't have to go that far because we're only going from negative 3 pi or 2 to 2 pi but we start dividing it up into four sections here's 3 pi over 2 here's negative 3 pi over 2 so that's what we're stopping okay and if you remember it starts at the top goes to the middle there the zero line the equilibrium line so so it's going to look this side's going to look like this and then it'll do the same thing on the other side.

01:45 And it's going to stop right there because that's all we have to graph.

01:49 So there's how you graph it by hand.

01:52 Now it says find the minimum and maximum values.

01:56 Well, that's where it's at its lowest points and its highest points.

02:00 So this red dot here and this red dot here are the minimum.

02:05 So the minimum points occur at.

02:15 So that'll be pi comma negative 6 and negative pi comma negative 6.

02:25 Those are the coordinates...