(a) Show that the point (2, 4) lies on the curve 2° +y° – 9xy = 0. Then find the tangent and normal to the curve there. (b) Water runs into a conical tank at the rate of 9 m³ /min. The tank stands point down and has a height of 10 mand a base radius of 5 m. How fast is the water level rising when the water is 6 m deep? (c) Suppose that it costs C(x) = x³ – 6x² + 15x dollars to produce r radiators when 8 to 30 radiators are produced and that R(x) = x³ – 3x² + 12x gives the dollar revenue from selling x radiators. Your shop currently produces 10 radiators a day. About how much extra will it cost to produce one more radiator a day, and what is your estimated increase in revenue for selling 11 radiators a day? (d) If æ + y = xy, show that y" = . (e) Evaluate y" for the ellipse bx? + a²y² = a²b°.
(a) Show that the point (2, 4) lies on the curve 2° +y° – 9xy = 0. Then find the tangent and normal to the curve there. (b) Water runs into a conical tank at the rate of 9 m³ /min. The tank stands point down and has a height of 10 mand a base radius of 5 m. How fast is the water level rising when the water is 6 m deep? (c) Suppose that it costs C(x) = x³ – 6x² + 15x dollars to produce r radiators when 8 to 30 radiators are produced and that R(x) = x³ – 3x² + 12x gives the dollar revenue from selling x radiators. Your shop currently produces 10 radiators a day. About how much extra will it cost to produce one more radiator a day, and what is your estimated increase in revenue for selling 11 radiators a day? (d) If æ + y = xy, show that y" = . (e) Evaluate y" for the ellipse bx? + a²y² = a²b°.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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