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Set y equal to zero and look at how the derivative behaves along the x-axis. Do the same for the y-axis by setting x equal to 0 Consider the curve in the plane defined by setting y = 0 -- this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and an be used to construct the direction field picture by hand. (2x + y) (2y) 2. y = 2y + x²e2x 1. y' = 3. y = e-*+ 2y 4. y = 2 sin(x) +1+y

Set y equal to zero and look at how the derivative behaves along the x-axis. Do the same for the y-axis by setting x equal to 0 Consider the curve in the plane defined by setting y = 0 -- this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and an be used to construct the direction field picture by hand. (2x + y) (2y) 2. y = 2y + x²e2x 1. y' = 3. y = e-*+ 2y 4. y = 2 sin(x) +1+y

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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A7:717 1,6 1 1,0 tit 1.8 T4 1,0 1:0 1 111
Transcribed Image Text:A7:717 1,6 1 1,0 tit 1.8 T4 1,0 1:0 1 111
A. Set y equal to zero and look at how the derivative behaves along the x-axis. B. Do the same for the y-axis by setting x equal to 0 C. Consider the curve in the plane defined by setting y = 0 -- this should correspond to the points in the picture where the slope is zero. D. Setting y equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and can be used to construct the direction field picture by hand. %3D 1. y'= (2x + y) %3D (2y) 2. y' = 2y + x²e2x %3D 3. y = e-x + 2y 4. y = 2 sin(x) +1+y -4 1 1 A 1.e 170 F4
Transcribed Image Text:A. Set y equal to zero and look at how the derivative behaves along the x-axis. B. Do the same for the y-axis by setting x equal to 0 C. Consider the curve in the plane defined by setting y = 0 -- this should correspond to the points in the picture where the slope is zero. D. Setting y equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and can be used to construct the direction field picture by hand. %3D 1. y'= (2x + y) %3D (2y) 2. y' = 2y + x²e2x %3D 3. y = e-x + 2y 4. y = 2 sin(x) +1+y -4 1 1 A 1.e 170 F4
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