Suppose that g(x, y) = x + y - 1 and f(x, y) = y =...

 

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Suppose that g(x, y) = x + y - 1 and f(x, y) = y = ax for some number a, and that you wish to find the point on the circle with equation g(x, y) = 0 at which f(x, y) is largest. Explain briefly how you know that at this point the slope of the tangent line to the level curve g(x, y) = 0 is a. (This can be answered with a few sentences explaining why the slope is a, or alternatively with a computation explicitly showing that is the slope.) [1 marks] Suppose that g(x, y) = x + y - 1 and f(x, y) = y = ax for some number a, and that you wish to find the point on the circle with equation g(x, y) = 0 at which f(x, y) is largest. Explain briefly how you know that at this point the slope of the tangent line to the level curve g(x, y) = 0 is a. (This can be answered with a few sentences explaining why the slope is a, or alternatively with a computation explicitly showing that is the slope.) [1 marks]