1.Let denote the slope of the tangent line to the curve . Find the instantaneous rate of change of the slope of the tangent line at .

2.A conical cup is 40 cm tall with a radius of 15 cm. The cup is being filled with water at a rate of cm/sec. How fast is the water level rising when the water level is 3 cm?

3.Find the area of the largest rectangle having two vertices on the x-axis and two vertices on or above the x-axis and on the parabola .

4.Determine the point on which f has relative extrema, the intervals at which f is increasing, the intervals at which f is decreasing, the point/s of inflection of f (if it exists). Also, determine where the graph of f is concave upward, and where the graph of f is concave downward. Sketch the graph of the curve