Lab 8
Name: Andrea Freeman
Section: 4
Exercise 1:
It is known from past experiments that the height (in feet) of a given plant after
t
months is given
approximately by
1/ 2
( )
6
3
H t
t
t
=

for
0 ≤ t ≤ 2
.
(a)
How long will it take a plant to reach its maximum height?
STEP 1 DEFINE FUNCTION AND FIND CRITICAL POINTS:
syms t
H = 6*(t^(1/2))  (3*t)
H =
6*t^(1/2)3*t
dHdt=diff(H,t)
pretty(dHdt);
critical_points = solve(dHdt,t)
dHdt =
3/t^(1/2)3
3
  3
1/2
t
critical_points =
1
c1=1
c1 =
1
*There is one critical point, which is at t=1 month.
STEP 2 CLASSIFYING CRITICAL POINTS WITH THE FIRST DERIVITIVE TEST:
fplot('[6*t^(1/2)3*t,3/t^(1/2)3]',[0,2])
title('Graph of Height of a given plant vs Time')
xlabel('Time in months')
ylabel('Height in feet and change of Height ft/mo')
legend('Height', 'Rate of change of height')
grid on
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Graph of Height of a given plant vs Time
Time in months
Height in feet and change of Height ft/mo
Height
Rate of change of height
*From the graphs we can see that t=1 month is a local maximum.
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 Fall '07
 MonicaHurdal

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