Question

What is the maximum height, And when does it occur? h(t)=-16t^(2)+80t+3. Please help.

Answer 1

the maximum height of this parabola is basically the vertex. so if you find the vertex, then there's your maximum height.

Answer 2

Have you learned about derivatives yet?

Answer 3

yes,

Answer 4

Find the derivative of your function, and set it equal to zero, and solve for t. That will tell you when it occurred.

Answer 5

So 0 = Derivative of function.

Answer 6

okay thx guys :)

Answer 7

If you stay on here, I can verify your work as you work through it.

Answer 8

is it f(0)=83 or (0,80)

Answer 9

Still solving that, but that doesn't seem correct.

Answer 10

ill keep trying.

Answer 11

Are you sure it's +80t and not -80t? From what I know, negative time doesn't exist.

Answer 12

Sorry, the other way around.

Answer 13

the problem says h(t)=-16t^(2)+80t+3

Answer 14

Aaaah! I see. When you posted your problem, the negative sign was cut off so all I saw was 16t^2

Answer 15

Alright, I solved it.

Answer 16

Where do you need help?

Answer 17

If you're just completely lost I can walk you through it.

Answer 18

that would help ALOT.

Answer 19

Sounds good!

Okay, so your function is f(t) = -16t^2 + 80t + 3
The derivative of that function is (df/dt) = -32t + 80

Does that make sense?

Answer 20

yess.

Answer 21

The function reaches its maximum height when the derivative, or the slope, is equal to zero.

It's kind of like when you throw a ball in the air. The moment the ball reaches the top of its arc, that's when the slope is zero.

So what you do is set the derivative to zero ...
-32t + 80 = (df/dt)
-32t + 80 = 0

Given that easy formula, solve for t and let me know what you get.

Answer 22

It's just algebra at this point.

Answer 23

does t= 5/2?

Answer 24

Yeah! Awesome!

Now, you plug that into h(t) and the number you get is your height.

Answer 25

And then you're done! :D

Answer 26

THANKS SO MUCH!

Answer 27

No problem :)

Answer 28

I HAve Another One or You.

Answer 29

*for