Which of the functions whose graphs are given below have a positive first derivative for all x? Choose the graphs which have a positive first derivative for all x. A. OB. [ c. D. Ay X XExplain why f(x) has a relative maximum at x =2. The function f(x) has a relative maximum at X: 2 because f'(2) = and f'(x) is VI for vaiues less than 2 and E for values greater than 2. zero positive negative Use the graph of f'(x), the derivative of f(x), given to the right to answer the following question. If f(5) = 9, what is the equation of the tangent line to the graph of y =1(x) at x: 5? The equation of the tangent line is Which of the functions whose graphs are given below have a negative second derivative for all x? Choose the graphs which have a negative second derivative for all x. A. OB. [c. OD. X XSketch the graph of a function that has the properties described below. f(2) = 1; f'(2) = 0; concave down for all x Choose the correct graph below. A. O B. O c. Ay O D. (1,2) Ay X (2.1) X (2,1) X (2,0) O E. OF. O G. OH. Ay Z, 1 (2,1) (2,0) X (1,2)Sketch the graph of a function that has the properties described below. f(4) = 2; f'(x) > 0 forx 0 and f'(x) > 0 for x>4. Choose the correct graph below. OA- OB. Y Q Y x a (4, 2) (4, ' I3 9,0 L'x.' 9 4, -2) L'x.' (4, 2) Use the given information to make a good sketch of the function f(x) near x = 4. {(4) = 5, f'(4)= 2, f\"(4) =1 Choose correct graph below. OA. Y Q (4, )k Q r3 :4 Use the given information to make a good sketch of the function f(x) near x = - 3. f( - 3) = 2, f'( - 3) = 0, f"'(- 3) = 2 Choose the correct graph below. O A. O B. O C. O D. Ay Ay (-3, 2 X (-3, 2)0 X (- 3, 2) X (-3, 2) XUse the graph below to fill in each entry of the grid with positive, negative or zero. y = f(x) f "' negative zero positiveSuppose that the graph to the right shows the graph of y y = s(t). the distance traveled by a car after t hours. Is the car 5 going slower at l = 8 or t = 10? p9 ISL At what time t is the car going slower? Choose the correct answer below. OA. OB. OC- on. The car is going slower at t: 8 because the slope of s(t) is smaller at t = 8. The car is going slower at t= 8 because the y-value of s(t) is smaller at t = 8. The car is going slower at t= 10 because the y-value of s(t) is smaller at t= 10. The car is going slower at t= 10 because the slope of s(t) is smaller at t = 10. Use the graph to the right to answer parts (a) through (1) below. I A (b) Looking at the values of f'(x) for 0 s x