[6] (20 pts) A curve is defined by the equation xy-y+4x+8=0. (a) Use implicit differentiation to...

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[6] (20 pts) A curve is defined by the equation xy-y+4x+8=0. (a) Use implicit differentiation to find dy/dx. (b) Compute the slope of the tangent line to the curve at the point (1,4). (b) (8 points) Determine the (absolute) maximum and minimum values for f(x) = x + 2x 6x on the closed interval [-1,2]. - [9] (20 pts) Find absolute extrema for the function f(x) = 9x-3x-x3 in the interval [-4,2]. [6] (20 pts) A curve is defined by the equation xy-y+4x+8=0. (a) Use implicit differentiation to find dy/dx. (b) Compute the slope of the tangent line to the curve at the point (1,4). (b) (8 points) Determine the (absolute) maximum and minimum values for f(x) = x + 2x 6x on the closed interval [-1,2]. - [9] (20 pts) Find absolute extrema for the function f(x) = 9x-3x-x3 in the interval [-4,2].