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Question 4 Consider the curve 5x²+4xy+4y³ = 29125 (a) Show that P(-75,-5) is on the curve i.e., show that P satisfies 5x²+4xy+4y³ (b) Find dy dx i.e., y'. (c) Determine the value of y' at P by... (i) using the expression in (b), and = (ii) substituting the coordinates of the point immediately after you carry out the differen- tiation in (b) (i.e, right before you start solving for the dy dx What do you observe? (d) A portion of the curve of 5x2 + 4xy+4y³ = 29125 is illustrated below.

Question 4 Consider the curve 5x²+4xy+4y³ = 29125 (a) Show that P(-75,-5) is on the curve i.e., show that P satisfies 5x²+4xy+4y³ (b) Find dy dx i.e., y'. (c) Determine the value of y' at P by... (i) using the expression in (b), and = (ii) substituting the coordinates of the point immediately after you carry out the differen- tiation in (b) (i.e, right before you start solving for the dy dx What do you observe? (d) A portion of the curve of 5x2 + 4xy+4y³ = 29125 is illustrated below.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 61E
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Question 4 Consider the curve 5x2+4xy+4y3 = 29125 (a) Show that P(-75,-5) is on the curve i.e., show that P satisfies 5x² + 4xy + 4y³ (b) Find dy dx i.e., y'. (c) Determine the value of y' at P by.... (i) using the expression in (b), and = 29125. (ii) substituting the coordinates of the point immediately after you carry out the differen- dy tiation in (b) (i.e, right before you start solving for the d) dx What do you observe? (d) A portion of the curve of 5x² + 4xy+4y³ 29125 is illustrated below. A D B E Which of the labelled points could be P(-75, -5)? Briefly justify your answer.
Transcribed Image Text:Question 4 Consider the curve 5x2+4xy+4y3 = 29125 (a) Show that P(-75,-5) is on the curve i.e., show that P satisfies 5x² + 4xy + 4y³ (b) Find dy dx i.e., y'. (c) Determine the value of y' at P by.... (i) using the expression in (b), and = 29125. (ii) substituting the coordinates of the point immediately after you carry out the differen- dy tiation in (b) (i.e, right before you start solving for the d) dx What do you observe? (d) A portion of the curve of 5x² + 4xy+4y³ 29125 is illustrated below. A D B E Which of the labelled points could be P(-75, -5)? Briefly justify your answer.
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