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y = 1 a(a²+3) (a-x), where a > 0 forms a triangle in the first quadrant with the - and y-axes. (a) Find the x- and y-intercepts of the line. Give your answers in terms of a. (b) What is the area of the triangle? Write your answer as a function of a. (c) Find the value of a such that the area is a maximum. Verify that your answer is a global maximum.

y = 1 a(a²+3) (a-x), where a > 0 forms a triangle in the first quadrant with the - and y-axes. (a) Find the x- and y-intercepts of the line. Give your answers in terms of a. (b) What is the area of the triangle? Write your answer as a function of a. (c) Find the value of a such that the area is a maximum. Verify that your answer is a global maximum.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The line y= 1 a(a² + 3) (a-x), where a > 0 forms a triangle in the first quadrant with the - and y-axes. (a) Find the x- and y-intercepts of the line. Give your answers in terms of a. (b) What is the area of the triangle? Write your answer as a function of a. (c) Find the value of a such that the area is a maximum. Verify that your answer is a global maximum.
Transcribed Image Text:The line y= 1 a(a² + 3) (a-x), where a > 0 forms a triangle in the first quadrant with the - and y-axes. (a) Find the x- and y-intercepts of the line. Give your answers in terms of a. (b) What is the area of the triangle? Write your answer as a function of a. (c) Find the value of a such that the area is a maximum. Verify that your answer is a global maximum.
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