Abox without a top is to be made from a rectangular piece of cardboard, with dimensions 11 in. by 16 in., by cutting out square corners with side length x and folding up the sides

• V = x(11 -2x)(16 -2x)

• x ≈ 2.1 in

Step-by-step explanation:

a) The volume of the box is the product of its depth (x), width (11 -2x) and length (16 -2x). The equation can be simply ...

v(x) = x(11 -2x)(16 -2x)

__

b) A graphing calculator can plot this equation directly. All that is needed is to enter it into the appropriate space provided by the calculator. The value of x that gives the greatest volume is the value that makes the function have a local maximum between x=0 and x=5.5 (where the volume is again zero).

That value of x is about 2.1 inches.

b.an increase in a causes b to decrease

gdp is the best phrase!