Height vs. volume The figure shows six containers, each of which is filled from the top. Assume that water is poured into the containers at a constant rate and each container is filled in 10 s. Assume also that the horizontal cross sections of the containers are always circ ? l?es. Let ? )be the depth of water in the contain?er at lim?e? for 0 ? ? ? 10. a. For each container, sketch a graph of t?he f?u?nction ?y =? ? ? )for 0 ? ?t ? 10. ?b. Explain why ?h is an increasing function. c. Describe the concavity of the function, Identify inflection points when they occur. d. For each? container, where d ? oes? ' (the derivative of? )have an absolute maximum on [0, 10]?

Solution: Step1 a. For each container, a graph of the function y = )for 0 t 10 Step2 (b) h is an increasing function because container is empty initially and water is...