Question

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 12 - x2? (4 points)

Answer 1

Answer: 16 square units

Explanation:

let the vertex in quadrant I be (x,y)

then the vertex in quadratnt II is (-x,y)

base of the rectangle = 2x

height of the rectangle = y

Area = xy

= x(12 - x²)

= -x³ + 12x

d(area)/dx = 3x² - 12 = 0 for a maximum of area

3x² = 12

x² = 4

x = ±2

y = 12-4 = 8

So, the largest area = 2 x 8 = 16 square units