Question 9 Given: f(x) =*+126x + 1202 - 2c". Find ALL interval(s) for which f(z) is INCREASING A (-oo, - 7) U (3,00) = (-7, 3) .(-00, – 3) U (7,00) none D A DB B
Question 11 10 pts The derivative f'(2) of an unknown function f(x) has been determined as f'(x) = (x - 2)(+3)2. Use this derivative to find the intervals where the original function f is increasing/decreasing. Then find the x-values that correspond to any relative maximums or relative minimums of the original unknown function f(x). O no relative maximum; relative minimum at x=2 relative maximum at x=-3; no relative minimum O relative maximum at x=2; relative minimum at x=-3 relative maximum...
The DERIVATIVE f'(x) of a function f(x) is given by f'(x) = x²(x - 3). Find the intervals on which the function f(x) is DECREASING OA (-2,0) and (3,00) OB. (-0,0) and (0,3) Oc (0,3) OD. (-0,0) OE (3,0)
Consider the function f(1) = 22 - 62+5 Answer all parts: (a) - (). (a) The vertex is (b) The axis of symmetry is (c) The 2-intercept(s) is (are) (Enter the list, separated by a comma. (d) The y-intercept is y = (e) Sketch a graph of f(x) = 22 - 61 +5. Instructions: To sketch the graph, click on the following locations: (1) vertex (2) the x--intercepts 10 10 0 -10 After graphing answer the following: (f) What is...
5 points) 1. Circle the correct answer. Use the graph of y = f(x) to solve f(x) < 0. A) (-2, 0) U (3,00) TVfx) B) (-2,0] [3,00) C) (-00, 2] U [0,3] D) (-00,-2) (0,3) E) none of the above
Question 8 (9 marks) For the function given by f(x) = are arctan(r3), find (a) dom(f) (b) dom(f'). (c) dom(f"). (d) Any stationary points of f. (e) The interval on which f is concave up. (f) The interval on which f is concave down. (g) Use parts (e) and (f) to determine whether f has an inflection point. Question 8 (9 marks) For the function given by f(x) = are arctan(r3), find (a) dom(f) (b) dom(f'). (c) dom(f"). (d) Any...
3. Consider the function f(x) = x2 - 6x^2 - 5 a. Find the values of x such that f'(x) = 0. b. Use the results of part a to: find interval(s) on which the function is increasing and interval(s) on which it is decreasing. c. Find the value(s) of x such that f"(x)=0. d. Use the result of part c to find interval(s) on which f(x) is concave up and interval(s) on which it is concave down. e. Sketch...
5. Given the function f(x)=x4 - 4x3 a) find f'(x) and the critical numbers of f. b) determine the interval(s) on which the graph off is increasing c) find f"(x) and the x-coordinates of the possible inflection points d) determine the interval(s) on which the graph off is concave down.
7. (10) a) Find F(s) 1) if f) -tet [u(t)-u(t-4)] 2) iffit) d/dt [t sin (at )] u(t) (15) b) Find f(t) 1) if F(s)-10 s/[(s+1)(s+5)] 2) İfF(s) 10 (s+3)/[s2 (s+2)] 3) if F(s) - 10/(s2+s+ 1) 7. (10) a) Find F(s) 1) if f) -tet [u(t)-u(t-4)] 2) iffit) d/dt [t sin (at )] u(t) (15) b) Find f(t) 1) if F(s)-10 s/[(s+1)(s+5)] 2) İfF(s) 10 (s+3)/[s2 (s+2)] 3) if F(s) - 10/(s2+s+ 1)
ESTION 6 (8 marks) Consider the function f(x) = 2 2+1 .) Find the interval(s) in which the function f(x) is increasing and the interval(s) in which the function is decreasing. b) Find the interval(s) in which the function f(x) is concave up and the interval(s) in which the function is concave down. c) Sketch the graph of the function f(x) ABC T T Arial 3 (12pt) T