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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.)

 

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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 (xy) =  (_____).

 

g has(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, or no extremum)at (xy) =  (_____).

 

g has(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, or no extremum)at (xy) =  (_____).

 

g has(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, or no extremum)at (xy) =  (_____).

 

 

 

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.

s”(
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 

r is 
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 

q = 
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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