The function f (x) = - (x-3) ^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

A) 3 square units

B) 6 square units

C) 12 square units

D) 9 square units

Question

Mathematics

Sophia Farmer

23 July, 01:53

The function f (x) = - (x-3) ^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

A) 3 square units

B) 6 square units

C) 12 square units

D) 9 square units

+1

Answers (1)

Know the Answer?

Douglas Dudley · Answer 1

D) 9 square units

Step-by-step explanation:

The squared term will always be non-negative, so the least it can be is zero (for x=3). The squared term is subtracted from 9, so the most the function value can be is 9.

The maximum area of the rectangle is 9 square units.

The function f (x) = - (x-3) ^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?A) 3 square unitsB) 6 square unitsC) 12 square unitsD) 9 square units

The function f (x) = - (x-3) ^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

A) 3 square units

B) 6 square units

C) 12 square units

D) 9 square units