FRQ on Differentiation

Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers a: for which 1' {I} is a real number. The table above gives selected values for a differentiable and decreasing function g and its derivative. Let f be the function with f {3] = 2 and derivative given by f1+ {as} = o: oos{e"'}_ {a} Find f" (sin 2}. Express your answer as a decimal approximation. (b) Let h be the function defined by h (x) = g (f (2x)). Find h (1.5). Express your answer as a decimal approximation.(c) Write an equation for the line tangent to the graph of g ], the inverse function of g, at a = -2.(d) The point (3, 1) lies on the curve in the xy-plane given by the equation (f (x)) +g(x) = xy - 1. What is the value of dy at the point (3, 1) ? Express your answer as a decimal approximation