Question

A foxhound jumps over the same hurdle. The table shows the height of the foxhound above the ground g(t), in inches, at t seconds:

Time (t) g(t)
0 0
0.4 5.44
0.6 6.24
0.7 6.16
0.8 5.76
1.0 4
1.2 0

How can I find the maximum of this table?

Answer 1

I need to interpret the maximum of the table before I can compare it to the maximum of f(t) = -16t^2 + 26t. But I don't remember how to find the maximum of tables. Can anyone help?

Answer 2

@aum

Answer 3

Go through the numbers in the second column and see which one is the largest and that will be the maximum.

Answer 4

So 6.24 at 0.6?

Answer 5

Yes, the maximum height reached by the foxhound is 6.24 inches and it occurs at t = 0.6 second.

Answer 6

And (0.8, 10.56) is the maximum of the formula.

Answer 7

So then, how does it want me to compare them? It only said this--Part A: Compare and interpret the maximum of f(t) and g(t)?

Answer 8

Er, function.

Answer 9

Your (0.81, 10.56) for the maximum of f(t) is correct.

Looks like g(t) and f(t) are two different functions. g(t) already start to decrease at 0.7 and 0.8 whereas f(t) keeps increasing at 0.7 and 0.8 until it reaches maximum at 0.81 second.

Answer 10

It wasn't 0.81, it was 0.8, according to the graph I created...unless that would be wrong.

Answer 11

Oh, typo?

Answer 12

It is actually 0.8125 to be exact. But it is hard to read higher decimal places from a graph.

Answer 13

Oh.I was using a graphing program, and it said (0.8, 10.56), so that was why I said that.

Answer 14

I did not read from a graph. I used calculus or you can find the vertex of a parabola (which is what f(t) is) and it will attain its maximum at t = 0.8125 second. But doesn't matter. They don't specify how many decimal places they want the answer to be.

Answer 15

So, for the comparing, you think it wanted me to talk about when it declined and/or something else?

Answer 16

Okay.

Answer 17

You can just say (0.6, 6.24) is the maximum for g(t) and
(0.8, 10.56) is maximum for f(t).
That is basically the comparison.

Answer 18

Oh. Then I'm done with that question, since I've already done the rest. Thanks!

Answer 19

I feel like I understand that much better now.

Answer 20

Can I try?!

Answer 21

@D3xt3R Sure! With what, exactly?

Answer 22

You are welcome.

IDK if they are expecting this but this is for your FYI.

When we are given the actual function, such as f(t) = -16t^2 + 26t, we can EXACTLY determine the maximum point.

When we are given a table we can only arrive at an approximation of the maximum point.
The table reaches a maximum of 6.24 at t = 0.6 after which it decreases to 6.16 at t = 0.7. But what happens at t = 0.61? at t = 0.62? Does it continue to increase a little more and then start to decrease. We can't be sure. So t = 0.6 is an approximation.

Answer 23

I see. That's actually pretty cool, because I didn't know about that.

Answer 24

Alright. Time to close this question.

Answer 25

I agree, although I think that Dexter wants your help.

Answer 26

...With another question? Because this one is done, Dexter.

Answer 27

...Yes or no?

Answer 28

Well, if it's with another question, then I do have a part of one. I'll put in a different question. I don't have that many left.

Answer 29

Does that sound good, or shouldn't I?

Answer 30

No worry, I tried to solve your question using a different way.

Answer 31

Oh. So you wanted to use a different method, and to participate. I see.

Answer 32

Well, thank you as well, I suppose.