11. A small independent motion picture company determines the profit P for producing n DVD copies of a recent release is P = -0.02n2 + 3.40n - 16, where P is the profit in thousands of
dollars and n is in thousands of units.
a. How many DVDs should the company produce to maximize the profit?
b. What will the maximum profit be?
12. A fireworks rocket is launched from a hill above a lake. The rocket will fall into the lake after
exploding at its maximum height. The rocket's height above the surface of the lake is given by g(x)=
-16x² +64x+80. What is the maximum height of the rocket?

hm let me think hm think think hm think yes

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: