1. The graph of the function y = x x is: {applet} Find the coordinates of its vertex and its intercepts. Select the correct answer:
vertex (2, - 4); x-intercepts 0, 4 ; y-intercept 0
vertex (3, 4); x-intercepts 0, 6 ; y-intercept 0
vertex (4, 8); x-intercepts 0, 3 ; y-intercept 0
vertex (- 2, - 3); x-intercepts 0, 6 ; y-intercept 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. The graph of the function y = x x + 10 is: {applet} Find its maximum or minimum value. Select the correct answer:
min = 9
min = - 10
max = 12
max = - 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. True or false: The local maximum and minimum values of the function f (x) = 3 x x and the value of x at which each occurs are: max = 1.15, x = , min = , x = 0.58.
True
False 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. A fish swims at a speed v relative to the water, against a current of 5 mph. Using a mathematical model of energy expenditure, it can be shown that the total energy E required to swim a distance of 13 miles is given by {image} Biologists believe that migrating fish try to minimize the total energy required to swim a fixed distance. Find the value of v that minimizes energy required. Select the correct answer:
7.5 15
8.5 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50