1. A bug crawls on the plane z = 2x +y, from the point (-2, 4, 0) to the point (2, 4, 8) along a path whose projection down on the x-y plane is the parabola y = x? (-2

Algebra and Trigonometry (MindTap Course List)
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Chapter12: Conic Sections
Section12.1: Parabolas
Problem 1E: A parabola is the set of all points in the plane that are equidistant from a fixed point called the...
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Pls help pls pls pls pls pls pls pls pls. Pls do all the parts. 

1. A bug crawls on the plane z = 2x + y, from the point (-2, 4, 0) to the point (2, 4, 8) along a path
whose projection down on the x-y plane is the parabola
y = x²
(-2 <x< 2).
Your job is to find the points at which its path is most steep or least steep, where steepness is
measured as the absolute value of the slope (as usual z is the vertical axis).
(a) Provide a technical analysis, finding the maximum and minimum of |m| where m is the slope of
its path.
(b) Explain how your solution could be obtained from a careful examination of the interaction
between the bug's path and the contour lines of the plane. You must include a diagram with your
explanation.
Transcribed Image Text:1. A bug crawls on the plane z = 2x + y, from the point (-2, 4, 0) to the point (2, 4, 8) along a path whose projection down on the x-y plane is the parabola y = x² (-2 <x< 2). Your job is to find the points at which its path is most steep or least steep, where steepness is measured as the absolute value of the slope (as usual z is the vertical axis). (a) Provide a technical analysis, finding the maximum and minimum of |m| where m is the slope of its path. (b) Explain how your solution could be obtained from a careful examination of the interaction between the bug's path and the contour lines of the plane. You must include a diagram with your explanation.
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