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1. find all of the critical points and local maximums and minimums of each function. (a) f(x) = 1+ 12 (b) f(x) = Vx -2, (c) f() = (d) f(x) = |x+5). 2. Find two numbers whose sum is 22 and whose product is as large as possible. (Suggestion: call the numbers r and 22 - c). 3. Find the value for x so the box shown below has the largest possible volume. 8-2x 8-2x 4. Find the coordinates of the point in the first quadrant on the circle, rty=1, so that the rectangle in the figure below has the largest possible area. x' + y = 1 (x, y) 5. Find the radius and height of the cylinder that has the largest volume (V = arch) if the sum of the radius and height is 9