Show all necessary steps to obtain full credits. 1. Find the local and absolute max and min of the function y = x - cos 2x on the interval [0, it] 2. Find the dimensions of the rectangular with the largest area that has its base on the x axis and its other two vertex above the x axis and lying on the parabola y = 1 - x2 3. Show the equation x' + x + 1 = 0 has exact one real solutions. 4. Given f (x) = X 2 - 4 find its domain, intercepts (if exist), asymptotes (if exist), critical points, interval of increasing/ decreasing, inflection point, interval of concavity, local max/min and then use these pieces of information to sketch the graph of f (x) = x2 - 1 X 2 - 4 5. Use Newton's method to find x1, and X2if f (x) = x - sinx with initial guess of xo = 1 (use radian mode in your calculator) 6. Find the anti-derivative of f (x) = sinx + 1 and f(0) = 1 and f' (0) = 2