Question

Directions: Answer each item accordingly. b.) Answer the following optimization problems systematically. 6.) Find two numbers whose difference is 50 and whose product is a minimum. 7.) Find the maximum profit (in Php) given that the profit function is P(x) = -x^4 + 2x^2 + 1. 8.) Find the point on the line y = 3x - 1 closest to the point (-1, 1). BONUS: a.) Answer the following optimization problem systematically. Find the dimensions of a rectangle with perimeter 200 m and whose area is as large as possible. 

          Directions: Answer each item accordingly.
b.) Answer the following optimization problems systematically.
6.) Find two numbers whose difference is 50 and whose product is a minimum.
7.) Find the maximum profit (in Php) given that the profit function is P(x) = -x^4 + 2x^2 + 1.
8.) Find the point on the line y = 3x - 1 closest to the point (-1, 1).
BONUS:
a.) Answer the following optimization problem systematically.
Find the dimensions of a rectangle with perimeter 200 m and whose area is as large as possible.
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Directions: Answer each item accordingly. b.) Answer the following optimization problems systematically. 6.) Find two numbers whose difference is 50 and whose product is a minimum. 7.) Find the maximum profit (in Php) given that the profit function is P(x) = -x^4 + 2x^2 + 1. 8.) Find the point on the line y = 3x - 1 closest to the point (-1, 1). BONUS: a.) Answer the following optimization problem systematically. Find the dimensions of a rectangle with perimeter 200 m and whose area is as large as possible.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Directions: Answer each item accordingly. b.) Answer the following optimization problems systematically. 6.) Find two numbers whose difference is 50 and whose product is a minimum. 7.) Find the maximum profit (in Php) given that the profit function is P(x) = -x^4 + 2x^2 + 1. 8.) Find the point on the line y = 3x - 1 closest to the point (-1, 1). BONUS: a.) Answer the following optimization problem systematically. Find the dimensions of a rectangle with perimeter 200 m and whose area is as large as possible.
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Transcript

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00:01 In this problem we are given difference between two numbers as 50.
00:03 So, x minus y equal to 50.
00:05 This implies y will be equal to x minus 50.
00:08 P of x is given as xy.
00:11 This can be written as x multiplied with x minus 50.
00:15 This is equal to x square minus 50x.
00:17 So we have to minimize the product.
00:20 P dash x will be equal to 2x minus 50.
00:23 Equating this to 0, we will 2x minus 50 is equal to 0.
00:28 This implies x is equal to 25 and thus y will be equal to 25 minus 50 which is equal to minus 25.
00:37 So these are the values of x and y for which the product is minimum...
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