Question

WILL FAN AND MEDAL

If ice forms for 0≤t≤30≤t≤3, at what time in this interval is the ice thickest? At what time is the ice forming fastest?

Ice is thickest at t=
Ice is forming fastest at t=

Answer 1

"0≤t≤30≤t≤3"
That doesn't make sense.

Answer 2

i meant 0≤t≤3

Answer 3

oh, i'm sorry i forgot to include that, At time t, in hours, a lake is covered with ice of thickness y cm, where y=0.3t^1.7

Answer 4

Find the derivative, set it equal to zero to find the maximum thickness.

Find the second derivative, set equal to zero, to find when it's forming fastest.

Answer 5

so the derivative is .51t^.7

Answer 6

.51t^0.7 = 0

Answer 7

there are no solution

Answer 8

It is true when t = 0

Then, once you have that value, don't forget to check the endpoint as well, t=3, by plugging into the original function. You want the largest value.

Answer 9

so when t = 0, the solution is 0

when t=3, the solution is .84

???

Answer 10

so then thickest at .84 and growing fastest at that point as well?

Answer 11

Not thickest AT 0.84. t is a time value. y is the thickness value. Make sure you know what you are finding.

For growing fastest you need second derivative... but i'm pretty sure it'll be fastest at t=3 as well.

Answer 12

so the second derivative is .36^-.3

Answer 13

Looks about right. And that'll never equal zero.

Answer 14

so increasing fastest is at t= 3 hours!

Answer 15

Yep, a graph would confirm both https://www.google.com/search?q=0.3t%5E1.7&rlz=1C1AOHY_enUS708US708&oq=0.3t%5E1.7&aqs=chrome..69i57&sourceid=chrome&ie=UTF-8

Kind of a very simple function to give for a question like this...

Answer 16

so i want the y value at x=.84

Answer 17

What...? You should know which value is which...

At t=3, what is the thickness y? It's not .84 btw.

Answer 18

oh wait i got confused XD the x value of 3 is where it is increasing fastest and y in the thickness

Answer 19

how do i get an exact value? i get something close to 2

Answer 20

Just don't simplify?

Answer 21

oh i got it, 1.942

(3,1.942)

Answer 22

wait, but it says t is thickest at a certain point. so it is thickest at t = 3 hours

Answer 23

i understand now XD

Answer 24

Looks right.