What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 - x2?
Accepted Solution
A:
The answer is 54 square units. 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(27 - x²) = -x³ + 27x d(area)/dx = 3x² - 27 = 0 for a maximum of area 3x² = 3 x 3² = 27 x² = 9 x = ±3 y = 27-9 = 18 So, the largest area = 3 x 18 = 54 square units