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Unformatted text preview: Math 17A
Discussion Sheet 6 1.) Use any method to differentiate the following functions. You need not simplify an-
swers. wwm b-)f($)=(m3+(x2+1)3)4 c.)f(m)=——(“’+5)3 (2‘3?)4
(1.) g(m)= (1:62:11)20 e.) f(m)=\/1+\/2+\/m 2.) Let : $(x — 5)4. a.) Solve f’(x) 2 0 for :13.
b.) Solve f”(x) = 0 for m. 3.) Assume that a pomegranate is projected directly upward from the ground withan
initial velocity of 112 ft. / sec. It can be shown that the pomegranate’s height above the
ground at time t seconds is given by .903) = —16t2 + 11215 feet. a.) What is the height of the pomegranate after t = 1 sec., t = 2 sec., and t = 5 sec.? b.) What is the velocity of the pomegranate after t = 1 sec., t = 2 sec., and t = 5
sec.? 0.) At What time does the pomegranate reach its maximum height ? What is the
pomegranate’s maximum height ? In how many seconds does the pomegranate strike the
ground ? d.) How long is the pomegranate in the air ? What is the pomegranate’s velocity as
it strikes the ground ‘? e.) What is the pomegranate’s acceleration when t = 1 sec., t = 2 sec., 13 = 5 sec. ? d d2
4.) Assume that y is a function of :13. Compute y’ = i and y” = 8—1: (You need not
m simplify y” for each equation. Write all answers in terms of a: and 3/ only. y=$2+$
c.) m2+y3=my 5.) Use implicit differentiation to ﬁnd the largest y—value in the “loop” of the Folium of
Descartes, which is given by the equation :33 + y3 — 3273/ = 0 (See diagram below.). Folium of Descartes 6.) Find the slope of the graph of my2 + y = 2 at :L' = 0 and at a: = 1 . Sketch the
graph near a: = 0 and a: = 1. 7.) The volume V of a sphere is changing at the rate of 7r ft.3 / min. At what rate is the
sphere’s surface area S changing when a.) S = 47r ft.2 ? b.) S = 367r ft.2 ?
(RECALL: For a sphere volume V = (4/ 3)7r7‘3 and surface area S = 47rr2.) 8.) Car B is 30 miles directly east of car A and begins moving west at 90 mph. At the same moment car A begins moving north at 60 mph. At what rate is the distance between 1
the cars changing after ,t = 3 hr. ? t= 5 hr. ? 9.) A conical tank (point down) has height 10 ft. and base radius 8 ft. Water begins
ﬂowing into the tank at the rate of 71' ft.3 / sec. At what rate is the depth h of the water
changing a.) when h = 1 ft. ? b.) when h = 9 ft. ?
(RECALL: For a cone volume V = (1/3)7rr2h.) +++++++++++++++++++++++++++++++++++++++++++ The following problem is for recreational purposes only. 10.) Find all points (cc, y) which are equidistant from the three given points (0, 0), (4, 0),
and (3, 2) . ...
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- Spring '08