For , the quantity represents the area, in square units, of a region whose linear…

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For

0 \le x \le 5

, the quantity

A(x)=x(10-2x)

represents the area, in square units, of a region whose linear dimensions depend on

x

. (a) Compute

A'(x)

. (b) Find all critical points of

A

in the interval

[0,5]

. (c) Determine the value of

x

that yields the maximum area and calculate that maximum. Justify your conclusion using an appropriate calculus test.