Understanding 3c 14 3 Part 7

Exploring 3c 14 3 Part 7 reveals several interesting facts. Implicit differentiation with partial derivatives: an explanation of the basic idea and a simple example.

Key Takeaways about 3c 14 3 Part 7

  • We look at a contour plot for the function we worked with in the previous video to see what the locations of max's, min's, and ...
  • We look at why the first derivative test for functions of one variable does not generalize to functions of more than one variable and ...
  • Finding the location and value of the absolute max and min of f(x,y) = xy on the unit disk. We first verify these exist using the ...
  • Finding the differential of a function. If asked to do this without being given a specific point and values for dx and dy, you are ...
  • We review the Extreme Value Theorem for real-valued functions of one variable and generalize it to real-valued functions of 2 or ...

Detailed Analysis of 3c 14 3 Part 7

Another example of finding all critical points for functions of 2 variables. Finding the location of the absolute max and min of a function of 2 variables. We first use the Extreme Value Theorem to ensure ... Another example: using the second derivative test to classify the critical points of the function we looked at in video 2 (#4 in your ...

An application problem: problem 50 from your text. We discuss how to know whether a max/min will exist if the Extreme Value ...

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