Question: For all x > 0, there is a unique value y = r(x) that solves the equation y 3 + 4xy = 16. (a) Show

For all x > 0, there is a unique value y = r(x) that solves the equation y³ + 4xy = 16.

(a) Show that dy/dx = 4y/(3y + 4x). (b) Let g(x) = f(x, r(x)), where f(x, y) is a function satisfying

(a) Show that dy/dx = 4y/(3y + 4x). (b) Let g(x) = f(x, r(x)), where f(x, y) is a function satisfying fx(1,2)=8, fy(1,2)= 10 Use the Chain Rule to calculate g' (1). Note that r(1) = 2 because (x, y) = (1, 2) satisfies y + 4xy = 16.

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