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TISSUE GROWTH Suppose a particular tissue culture has area AA(tt) at time tt and a
potential maximum area MM. Based on properties of cell division, it is reasonable to assume that
the area AA grows at a rate jointly proportional to �AA(tt) and MM − AA(tt); that is
dddd
dddd = kk�AA(tt) [MM − AA(tt)]
where kk is a positive constant.
a. Let RR(tt) = AA′
(tt) be the rate of tissue growth. Show that RR′
(tt) = 0 when AA(tt) = MM/3.
b. Is the rate of tissue growth greatest or least when AA(tt) = MM/3? [Hint: Use the first
derivative test or second derivative test.]
c. Based on the given information and what you discovered in part (a), what can you say
about the graph of AA(tt)?
The derivative of a differentiable function ff(xx) is given as
ff′
(xx) = xx + 3
(xx − 2)2 .
a. Find intervals of increase and decrease for ff(xx).
b. Determine values of xx for which relative maxima and minima occurs on the graph of
ff(xx).
c. Find ff′′(xx) and determine intervals of concavity for the graph of ff(xx).
d. For what values of xx do inflection points occur on the graph of ff(xx).
BLOOD CIRCULATION Poiseuille’s law asserts that the speed of blood that is rr
centimeters from the central axis of an artery of radius RR is SS(rr) = cc(RR2 − rr2), where cc is a
positive constant. Where is the speed of the blood greatest?
Suppose that a population yy grows according to the logistic model given by formula:
yy = LL
1 + AAee−kkkk .
a. At what rate is yy increasing at time tt = 0 ?
b. In words, describe how the rate of growth of yy varies with time.
c. At what time is the population growing most rapidly?
How to calculate cos x from its nth term in Maclaurin series??
A box with a square base is taller than it is width. In order to send the box through the
PH mail, the height of the box and the perimeter of the base can sum to no more than
108 in. What is the maximum volume for such a box?
from the top of the building 256 ft high an object is thrown vertically upward with an initial velocity of 96 ft/sec. when will it strike the ground?
show that when a body is dropped from a height h ft above the ground, its velocity v (neglecting air resistance) when it strikes the ground will be v=√2gh where g=32ft/sec^2.
On the moon the acceleration of gravity is 1.6 m/sec2. If a rock is dropped into a crevasse, how fast will it be going just before it hits the bottom 30 seconds later.
With what velocity must an object. Be thrown vertically upward or authority in the maximum height of 900ft from its starting point.
