Answer the following questions: Multiple choice

12. How many of the integers from 1 to 100, inclusive, have at least one digit equal
to 6?
(A) 17    (B) 18    (C) 19    (D) 21    (E) 22

13. Mayar and Rosie are 90 metres apart. Starting at the same time, they run towards
each other. Mayar runs twice as fast as Rosie. How far has Mayar run when they
meet?
(A) 15 m    (B) 30 m    (C) 45 m    (D) 60 m    (E) 75 m

14. Dhruv is older than Bev. Bev is older than Elcim. Elcim is younger than Andy.
Andy is younger than Bev. Bev is younger than Cao. Who is the third oldest?
(A) Andy    (B) Bev    (C) Cao    (D) Dhruv    (E) Elcim

15. How many of the integers 19, 21, 23, 25, 27 can be expressed as the sum of two prime
numbers?
(A) 3   (B) 4   (C) 1    (D) 2    (E) 5

4. (16 pts) MULTIPLE CHOICE! CIRCLE THE CORRECT ANSWER IN EACH PART. (I) ( 4 pts) Complete the statement of the Intermediate Value Theorem: Suppose f is continuous on the interval [a, b] and L is a number between f (a) and f (b). Then there is at least one number c in (a, b) such that (a) C = L; (b) f(c) = 0; (c) f(c) = L; (a) f' (c) = L; (e) C = 0; (f) f (a) < c < f (b); (g) NONE OF THE PREVIOUS ANSWERS. (II) (4 pts) The figure shows the graph of a function f. At what point (points) c does the conclusion of the Intermediate Value Theorem hold for f (x) on the interval [1, 5] and L = 2. --- - - - -1 - - - 2 - - I- - - (a) c = 1; (b) C = 0; (c) C = 2; (a) c = 3; (e) C = 4; (f) C = 5; (g) c= -1. (III) (4 pts) Given that cos x s f (x) s et, for all x > 0 evaluate lim f (x) x+0+ (a) lim f (x) = 0; (b) lim f (x) = 1; (c) lim f (x) = e; x0+ X0+ (d) lim f(x) DOES NOT EXIST. WE DON'T HAVE ENOUGH INFORMATION TO ANSWER THE QUESTION *40+ (IV) (4 pts) Given the function 1 f (x) = , find its inverse, f+(x) x -2 (a) f (x) = x -2; (b) f«+ (x) = x+2 ; (c) fº+ (x) = -2; (f) f-+ (x) -2; (e) f (x) DOES NOT EXIST.

2. (20 pts) An object begins moving along a vertical line at time t = Os and stops at time t = 6 s. Its height above the ground at time t is given by h(t) in the provided graph, where h is measured in meters. Use the graph to answer the following questions. on 0 (a) Compute the average velocity of the object on the time interval [0,6). Show your work. N 1 2 3 4 5 6 (b) Circle the choice that best describes the shape of the graph on the time interval (5,6). i. increasing and concave up ii. increasing and concave down iii. decreasing and concave up iv. decreasing and concave down (c) At what time is the object farthest away from the ground? What is the velocity at that time? time= velocity= (d) The maximum velocity attained on (0,6) occurs at one of the following times. Circle the correct choice. i. ls ii. 2 s iii. 3s iv. 4s v. 5s (e) Estimate the value of the maximum velocity attained. The value is an integer. (f) Let v(t) be the velocity at time t. Circle the greatest value amongst the following choices. i. v(2.5) ii. (2.6) ii. v(2.7) iv. v(2.8) V. (2.9) (8) List the time interval(s) on which the velocity is increasing. Use integer endpoints. (h) The maximum speed attained on (0,6) occurs at one of the following times. Circle the correct choice. i. ls ii. 2s iii. 35 iv. 4s v. 5s

1. (18 pts) Let f be the function with domain (-1,6) given by the graph below. 2 y =f(x) 1 2 3 4 5 6 -31 Use the graph of f to answer the following questions. (a) Order the following four numbers from smallest to largest: f'(-0.3), f'(O), f'(2.9), f'(4). (b) List the critical point(s) of f on the interval (-1,6). Write "none" if appropriate. (c) List the x-coordinates(s) at which f has a local maximum. Write "none" if appropriate. (d) List the x-coordinates(s) at which f has a local minimum. Write "none" if appropriate. (e) List the x-coordinates(s) at which f has a absolute maximum. Write "none" if appropriate. (f) List the x-coordinates(s) at which f has a absolute minimum. Write "none" if appropriate.