2.6 Question 7

[Eigenvalue]

Precalculus
Michael Sullivan
Edition 4
Chapter 2, Section 2.6

A rectangle has one corner in quadrant I on the graph y=16-x², another on the origin, a third on the positive y-axis, and the fourth on the positive x-axis

a) Express the area A as a function of x

b) What is the domain of A

c) Graph A(x); for what values of x is A largest

[Eigenvalue]

The area of the rectangle, A, is the product of the base and the height:
x is the base
y is the height
A=xy

Rewrite y as 16-x²
A=x(16-x²)=-x³+16x

a) A(x)=-x³+16x

b) The domain of x is all real numbers as the domain of all cubic functions is all real numbers.

See attachment