9. (a) Find the points at which the function 1 f(x) = ·x² (6 − x). - attains a local maximum or minimum. You do not have to say whether they are maxes or mins. (b) Use this information to help you draw the graph y = f(x) on the axes at the right. -8- -7 6. 5. 4 3 2 1- -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -1- --2- -3. --4-

If xis large, which function grows faster, f(x)=2x or g(x)=x2?

During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?

In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Minimizing Time A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point Pon the opposite bank and then walks the remaining distances x to B, as shown in the figure. He can row at a speed or 2 mi/h and walk as a speed of mi/h (a) Find a function that models the time needed for the trip. (b) Where should he land so that he reaches B as soon as possible?