You are standing in the Uffizzi gallery admiring a painting by Botticelli. The painting is huge, and your viewing location is pictured below; all measurements are in meters. o (a) If x is the your distance from the wall holding the painting, find a function A(x) that computes the angle a in the picture; A(x)= (b) Find the rate of change with respect to x of the angle a when you are at the location x (c) Find the rate of change with respect to x of the angle a when you are at the location x=4 m. (Exact answer.) (d) Find the rate of change with respect to x of the angle a when you are at the location x=13 m. (Exact answer.) (e) Find the location where the rate of change with respect to x of the angle a is zero m.(Exact answer.) (f) When you are standing at the location to maximize a, what is the value of a? (Radians to three decimal places.) The graph of the equation 2x2 + xy + y2 = 4 is the tilted ellipse pictured below; i.e. the points (x,y) in the plane that satisfy the equation yield the pictured ellipse. This is NOT the graph of a function y=fx). However, if you solve the original equation for v in terms of x, you can break the graph into two pieces, each of which is the graph of a function as pictured below. (a) The upper piece of the ellipse (solid) is the graph of the function y=g(x}= (b) The lower piece {dashed) of the ellipse is the graph of the function y=h{x)= (c) There are two points indicated (as big dots) where the graphs of the functions in (a) and (b) "glue together\". What is the x-coordinate of the right-most point? (d) The implicit derivative is dy/dx= (e) Setting the denominator of (d) equal to zero yields the linear equation: y= X (fiSimultaneocusly solving (e) with the original equation gives lx|= The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x* + 4y