Suppose that x and y are related by the equation x3y7 x y

Question

MATH 16A WORKSHEET 9-

(1) Find the minimum of x + y where x ∈ [0, 1] and y = √(1 - x²).

(2) Find f'(2) where f(x) = √e^x/(x-1)² .

(3) Let g be a differentiable function such that g'(0) = -3, and define f(x) = g(x(x + 1)⁴). Find f'(0).

(4) Suppose that x and y are related by the equation x³y⁷ = x + y + 1 and use implicit differentiation to determine dy/dx.