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# Differentiation graph

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297
24 Find the values of t for which the height of the water is decreasing.

I tried typing in the graph on desmos expecting a cubic graph but it just gave me a straight line

Dec 17, 2018

#1
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That is where the graph caught you off guard! The graph is actually not a straight line. Zoom out, and you will see that the graph curves like an "N" at around y = 58!

- PM

Dec 17, 2018
#4
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unfortunately the reason why i typed it in to desmos is i thought there would be roots to help me solve it but the range is a bit far for me haha

YEEEEEET  Dec 17, 2018
edited by YEEEEEET  Dec 17, 2018
#5
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So there you have it... the height of the water decreases around \(t = 2.25\).

Hope this helps,

- PM

PartialMathematician  Dec 17, 2018
edited by PartialMathematician  Dec 17, 2018
#3
+4

Take the derivative

h ' =   12t^2 - 59t + 72

Set this to 0    and set to 0

12t^2 - 59t + 72 =  0

(4t -9) (3t - 8) = 0

Setting both factors to 0 and solving for x gives

t = 9/4          t  = 8/3

Take the second derivative

24t - 59

Plugging   9/4 into this gives   - 4....so....we have a max at  t = 9/4 sec = 2,25 sec

Plugging  8/3 into this  gives  5....so....we have a min at t = 8/3 sec = 2.66 sec

So...the water height is decreasing from  2.25 sec to 2.66 sec

Heres the graph : https://www.desmos.com/calculator/ne2dnm3tks

YEEEEEET.......This does look like a straight line if you don't "zoom in"....very subtle....!!!!   Dec 17, 2018
#6
+1

ahhh ok thank you very much

YEEEEEET  Dec 17, 2018
#7
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You are welcome! (I didn't exactly do much)

PartialMathematician  Dec 17, 2018
edited by PartialMathematician  Dec 17, 2018