FIGURE IT OUT!

1. Look at the graph below. Starting at square X, Judy hopped 4 squares up and 3 squares to the right. In which square did she land?

NOTE: Judy and Rudy can hop in vertical and horizontal directions only.

2. Rudy is in square X. Which are the 2 shortest paths he can take to get to square E?

3. Judy is in square A. Which are the 2 shortest paths she can take to get to square E?

4. Find the 2 shortest paths to get from square X to square D.

5. Starting at square X, Rudy hopped 6 squares up and 5 squares to the left. How many squares is he from square D?

 

*Please refer to the attached file

48 f(x) = 12 + (x + 1)2 4. (22 pts) The function f, its derivative f', and its second derivative f" are given by the expressions below. f'(x) = -96(x+1) (12+(x + 1)2) (12+(x + 1)2) (a) Circle the correct statement. f"(x)288(x2 + 2x - 3) i. f is even ii. f is odd. iii. f is neither even nor odd. (b) Give an equation for each horizontal asymptote of f. Write "none" if appropriate. Show your work. Show work for parts (c), (d), (e), and (f) in the space below. (c) List the interval(s) on which f is increasing. Write "none" if appropriate. (d) List the interval(s) on which f is decreasing. Write "none" if appropriate (e) List the x-value(s) at which the local minima of f occur. Write "none" if appropriate (f) List the x-value(s) at which the local maxima of f occur. Write "none" if appropriate. (8) List the interval(s) on which f is concave up. Write "none" if appropriate. (h) List the interval(s) on which f is concave down. Write "none" if appropriate. (i) List the x-coordinate(s) of the inflection points of f. Write "none" if appropriate. () Sketch the graph of y = f(x). Mark the locations of any local extrema and/or inflection points with filled-in circles. Your sketch should be consistent with your answers to (a)-0). -10 -9 -8 -7 -6 -5 -4 4 5 6 7 8 9 10

1. (45 marks) Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers in this question. a) Find the equation of the tangent plane to the graph of the function z = f(x,y) = sell at (0,1). Answer b) Evaluate (T, 0) if f(x,y) = sin(ry). Answer c) Graph of a function z = f(x,y) is given by: Which of the following level curves correspondes to this function. Answer d) If f(x,y) = e(3x – 2y), find lim - Math)-f(x,y) e) Find % if f(x, y) = x2 - y3 and 2 = r sin(t), y = r cos(t). Answer f) Evaluate the directional derivative of f(x, y) = !at (1, -1) in the direction of u =(2, 1). Answer 8) Does Simono converge? h) Sketch the direction field of the differential equation = 1-2y. i) Consider the differential equation ay = 15 - 31, y(0) = 0, and use Euler's method with step size 0.1 to estimate y(0.1). Answer j) Knowing that (-3,-3) is a critical point of f(x,y) = 2:3 + y2 – 4.cy -3.0, use the second derivative test to find out whether it is a local minimum, local maximum, or a saddle point. Answer k) Solve the initial value problem, dy dt 642 2y + cos(u) y(1) = . Answer 1) Is ū=(2,2, -1) perpendicular to v = (5,-4, 2)? Answer m) Find the area between the graph of y = 1 + sin(x) and y=1-sin(x) from 0 to 7. Answer n) Determine the lentgh of the curve y = 8/2,0 SIS 3. Evaluate and simplify your answer. Answer o) Express the volume of the solid obtained by rotating the bounded region that lies between curves y = (x-2)2 and y=1,150 $4 about the vertical line 2 = 5. Do not evaluate this integral. Answer

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