Some useful trigonometric identies and logarithmic identities can be found below. You will find a formula how to complete the square for a quadratic as well. Find the local extrema, classify them, find the intervals where f is increasing or decreasing, find inflection points, intervals where f is concave up or down.
Water is inside a cone.
Show the water level drops at a constant rate independent of the dimensions of the cone. Find the local extrema, classify them, find the intervals where f is increasing or decreasing, find inflection points, intervals where f is concave up or down. Find and classify the local extrema. The cost of making the bottom of the can is three times the cost of making the side of the can. Find the radius and the height of the can that would minimize the cost.