calc questions

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.

(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 

Round your answer to two decimal places.)

_______cm/s

5. The weekly sales of Honolulu Red Oranges is given by 

 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.

$_____