Question

The area of a planned garden can be modeled by the equation A= -4w2 + 64w,

where w is the width of the garden in feet. Someone please help

Answer 1

Maximum Width = 8 feet.

Maximum area = 256 ft^2.

Explanation:

Part A.

A = -4w^2 + 64w

Finding the derivative:

dA/dw = -8w + 64 = 0 for maxm/minm, so

-8w = -64

w = 8

The second derivative is -8 so w = 8 gives a maximum.

Part B.

The maximum area = -4(8)^2 + 64*8

= -256 + 512

= 256 ft^2.

Answer 2

8 feet, 256 ft^2

Explanation:

The function of the area can be graphically rapresented with a parabola that opens downwards

in this specific case the vertex is the maximum point of the parabola.

(X) Vertex = -64/-8 = 8 feet

(Y) Vertex = -4(64) + 512 = -256 + 512 = 256 ft^2