18_Cal_Solution of Calculus_6e

18_Cal_Solution of Calculus_6e - C01S02.066: Recall that...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: C01S02.066: Recall that the area of the rectangle is given by y = A ( x ) = x (50 − x ). To maximize A ( x ) we find the vertex of the parabola: y = 50 x − x 2 = − ( x 2 − 50 x ) = − ( x 2 − 50 x +625 − 625) = − ( x − 25) 2 +625. Because the vertex of the parabola is at (25 , 625) and x = 25 is in the domain of the function A , the maximum value of A ( x ) occurs at x = 25 and is A (25) = 625 (ft 2 ). C01S02.067: If two positive numbers x and y have sum 50, then y = 50 − x and x < 50 (because y > 0). To maximize their product p ( x ) we find the vertex of the parabola y = p ( x ) = x (50 − x ) = − ( x 2 − 50 x ) = − ( x 2 − 50 x + 625 − 625) = − ( x − 25) 2 + 625 , which is at (25 , 625). Because 0 < 25 < 50, x = 25 is in the domain of the product function p ( x ) = x (50 − x ), and hence the maximum value of the product of x and y is p (25) = 625. C01S02.068: Recall that if x new wells are drilled, then the resulting total production p is given by...
View Full Document

This note was uploaded on 09/14/2011 for the course MATH 101 taught by Professor Cheng during the Spring '11 term at Ecole Hôtelière de Lausanne.

Ask a homework question - tutors are online