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Chapter 2: Q. 41 (page 125)

A rectangle has one vertex in quadrant 1st on the graph of y=10-x2, another at the origin, one on the positive x-axis, and one on the positive y-axis.

(a) Express the area Aof the rectangle as a function of x.

(b) Find the largest area Athat can be enclosed by the rectangle.

Short Answer

Expert verified

(a) The area of the rectangle as a function of xis 10x-x3.

(b) The largest area is 12.1716123890037

Step by step solution

01

Step 1. Part (a) Find the area A of the rectangle as a function of x.

The area of the rectangle is xy

Substitute y=10-x2

A=x10-x2A=10x-x3

02

Step 2. Part (b) Find the largest area A that can be enclosed by the rectangle.

This is the graph of A, so the largest area islocalid="1645957871121" 12.1716123890037

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