calc questions
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Find the exact location of all the relative and absolute extrema of the function. HINT [See Example 1.] (Order your answers from smallest to largest x.)
g(x) = 6x3 − 72x with domain [−4, 4]
g has(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, or no extremum)at (x, y) = (_____).
g has(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, or no extremum)at (x, y) = (_____).
g has(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, or no extremum)at (x, y) = (_____).
g has(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, or no extremum)at (x, y) = (_____).
2. For reasons too complicated to explain, I need to create a rectangular orchid garden with an area of exactly 169 sq. ft. abutting my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs $2 per foot. What are the dimensions of the orchid garden with the least expensive fence?
south fence _____________ft
east and west fence ______________ ft
3. The position s of a point (in feet) is given as a function of time t (in seconds).
s = 3/t – 3/t^2; t = 2
(a) Find its acceleration as a function of t.
t) = ____________ft/sec
2
(b) Find the point’s acceleration at the specified time.
s”(2) = ______ ft/sec2
4. A rather flimsy spherical balloon is designed to pop at the instant its radius has reached 6 centimeters. Assuming the balloon is filled with helium at a rate of 14 cubic centimeters per second, calculate how fast the radius is growing at the instant it pops. HINT [See Example 1.] (The volume of a sphere of radius
V = 4/3
π
r
3.
Round your answer to two decimal places.)
_______cm/s
5. The weekly sales of Honolulu Red Oranges is given by
1,120 −
10
p
Calculate the price elasticity of demand when the price is $32 per orange (yes, $32 per orange†) ___________________
Interpret your answer. The demand is going ____ by %____ per 1% increase in price at that price level.
Also, calculate the price that gives a maximum weekly revenue.
$_____
Find this maximum revenue.
$_____
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