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Consider a differentiable function p(x,y) with the properties below. Use these properties to answer the questions. Px(1,4)= 6, Py(1,4) = -5, and p(1,4) = 12 (c) Find a vector in the xy-plane that is tangent to the level curve of p(x,y) at (1,4).. (b) Find a vector of length4 that is normal to the surface of p(x,y) at (1,4,12). (a) Find the minimum rate of change of p(x,y) at (1, 4). Hint: the answer is not 0. (d) Find the slope on the surface of p(x,y) at (1,4) if we head in the direction that makes an angle of with the positive x-axis.

Consider a differentiable function p(x,y) with the properties below. Use these properties to answer the questions. Px(1,4)= 6, Py(1,4) = -5, and p(1,4) = 12 (c) Find a vector in the xy-plane that is tangent to the level curve of p(x,y) at (1,4).. (b) Find a vector of length4 that is normal to the surface of p(x,y) at (1,4,12). (a) Find the minimum rate of change of p(x,y) at (1, 4). Hint: the answer is not 0. (d) Find the slope on the surface of p(x,y) at (1,4) if we head in the direction that makes an angle of with the positive x-axis.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a differentiable function p(x,y) with the properties below. Use these properties to answer the questions. Px(1,4) = 6, py(1,4)= -5, and p(1,4) = 12 (c) Find a vector in the xy-plane that is tangent to the level curve of p(x,y) at (1,4).. (b) Find a vector of length 4 that is normal to the surface of p(x,y) at (1,4,12). (a) Find the minimum rate of change of p(x,y) at (1, 4). Hint: the answer is not 0. (d) Find the slope on the surface of p(x,y) at (1,4) if we head in the direction that makes an angle of with the positive x-axis.
Transcribed Image Text:Consider a differentiable function p(x,y) with the properties below. Use these properties to answer the questions. Px(1,4) = 6, py(1,4)= -5, and p(1,4) = 12 (c) Find a vector in the xy-plane that is tangent to the level curve of p(x,y) at (1,4).. (b) Find a vector of length 4 that is normal to the surface of p(x,y) at (1,4,12). (a) Find the minimum rate of change of p(x,y) at (1, 4). Hint: the answer is not 0. (d) Find the slope on the surface of p(x,y) at (1,4) if we head in the direction that makes an angle of with the positive x-axis.
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