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Find dy/dx and d?y/dx², and find the slope and concavity (if possible) at the given value of the para Parametric Equations Point x = 4 cos 0, y = 4 sin 0 4 Part 1 of 6 You know that the parametric form of the derivative is dy/ do de dy dx = -4 sin (0) dx Part 2 of 6 Consider the parametric equation y = 4 sin 0. Differentiating gives dy de d (4 sin 0) de 3D 4 cos(0) 4 cos (0) Part 3 of 6 Now consider the parametric equation x = 4 cos 0. Differentiating gives dx d (4 cos 0) de de -4 sin(0) -4 sin (0) Part 4 of 6 Simplify. 4 cos 0 -4 sin 0 dy dx -cot(0) - cot (0 Part 5 of 6 Now, we can find the second derivative. (dy/dx) dx2 (-cot 0) de OP/xp

Find dy/dx and d?y/dx², and find the slope and concavity (if possible) at the given value of the para Parametric Equations Point x = 4 cos 0, y = 4 sin 0 4 Part 1 of 6 You know that the parametric form of the derivative is dy/ do de dy dx = -4 sin (0) dx Part 2 of 6 Consider the parametric equation y = 4 sin 0. Differentiating gives dy de d (4 sin 0) de 3D 4 cos(0) 4 cos (0) Part 3 of 6 Now consider the parametric equation x = 4 cos 0. Differentiating gives dx d (4 cos 0) de de -4 sin(0) -4 sin (0) Part 4 of 6 Simplify. 4 cos 0 -4 sin 0 dy dx -cot(0) - cot (0 Part 5 of 6 Now, we can find the second derivative. (dy/dx) dx2 (-cot 0) de OP/xp

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 62E
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Find dy/dx and d?y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations Point x = 4 cos 0, y = 4 sin 0 4 Part 1 of 6 You know that the parametric form of the derivative is dy/ do de dy dx = -4 sin (0) dx Part 2 of 6 Consider the parametric equation y = 4 sin 0. Differentiating gives dy de d (4 sin 0) de 3D 4 cos(0) 4 cos (0) Part 3 of 6 Now consider the parametric equation x = 4 cos 0. Differentiating gives dx d (4 cos 0) de de -4 sin(0) -4 sin (0) Part 4 of 6 Simplify. 4 cos 0 -4 sin 0 dy dx -cot(0) - cot (0 Part 5 of 6 Now, we can find the second derivative. d?y dx2 dy/dx) (-cot 0) OP/xp -4 sin 0
Transcribed Image Text:Find dy/dx and d?y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations Point x = 4 cos 0, y = 4 sin 0 4 Part 1 of 6 You know that the parametric form of the derivative is dy/ do de dy dx = -4 sin (0) dx Part 2 of 6 Consider the parametric equation y = 4 sin 0. Differentiating gives dy de d (4 sin 0) de 3D 4 cos(0) 4 cos (0) Part 3 of 6 Now consider the parametric equation x = 4 cos 0. Differentiating gives dx d (4 cos 0) de de -4 sin(0) -4 sin (0) Part 4 of 6 Simplify. 4 cos 0 -4 sin 0 dy dx -cot(0) - cot (0 Part 5 of 6 Now, we can find the second derivative. d?y dx2 dy/dx) (-cot 0) OP/xp -4 sin 0
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