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Solution: Directions of change Consider the following
Chapter 11, Problem 33E(choose chapter or problem)
Directions of change Consider the following functions f and points P. Sketch the xy-plane showing P and the level curve through P. Indicate (as in Figure 12.70) the directions of maximum increase, maximum decrease, and no change for f.
\(f(x, y)=8+4 x^{2}+2 y^{2} ; P(2,-4)\)
Questions & Answers
QUESTION:
Directions of change Consider the following functions f and points P. Sketch the xy-plane showing P and the level curve through P. Indicate (as in Figure 12.70) the directions of maximum increase, maximum decrease, and no change for f.
\(f(x, y)=8+4 x^{2}+2 y^{2} ; P(2,-4)\)
ANSWER:Solution 33E
Step 1 of 2
Gradient is defined as the rate of change of the function. It is denoted as for a function.
Level curve of a function is the family of curves for any c such that.