Draw a graph to match the description given. F(x) has a positive derivative over (-0,1) and...
The DERIVATIVE F"(x) of a function f(x) is given by X f'(x)= 1 + x + 2x3 What is the x-coordinate of the inflection point of the graph of f(x)? O A. X = 0.393 OB. X= -1.607 O c. X=0 OD. The graph off has no inflection point. O E. X = 0.807
The graph of a logarithmic function is given. Match the graph to its function Which function matches the graph? O A. ys - logs - x) OC. y log six-1) OE y = logs(X) OG y = 1 - logs OB y = logsx-1 OD, y logs OFylogs OH y = log (1-x)
The graphing calculator window shows the graph of a function f(x) and its derivative function f(x). Decide which is the graph of the function and which is the graph of the derivative. Which of the following methods would be helpful in distinguishing the graph of the function from the graph of its derivative? O A. Compare the x-intercepts of each line to see if a horizontal tangent line occurs at that x-value on the other line. Y2 O B. Calculate...
Suppose that a continuous function f has a derivative f' whose graph is shown below over the interval (4, 13). y=f'(x) 1 2 3 4 5 6 7 8 9 10 11 12 13 (a) Find the interval(s) over which f is increasing. (Enter your answer using interval notation.) (4, 6)U(7, 9) U (11, 13) Find the interval(s) over which f is decreasing. (Enter your answer using interval notation.) (6, 7) U (9, 11) (b) Find the x-value(s) where f...
(1 point) The given graph of the derivative f' of a function f is shown. Assuming the graphs continue in the same way as x goes to infinity and negative infinity, answer the following questions. 1. On what intervals is f increasing? Answer (in interval notation): [-3.2,-1]U[2.5,Inf) 2. On what intervals is f decreasing? Answer (in interval notation): (-Inf,-3.2]U[-1,2.5] Note: You can click on the graph to enlarge the image.
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)
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
The graph of y=f(x) is shown to the right. Identify the intervals on which f(x) is increasing 1h Which of the following shows every interval on which f(x) is increasing? Choose the correct answer below A. (b.c), (e,t). (g.h) O C. (5.c), (0,1),(g,h) OB. (a.c), (e.f). (g.h) OD. (a.c), (d.1)
Find the average value of the following function over the given interval. Draw a graph of the function and indicate the average value. f(x) = x(x - 1); (5,81 The average value of the function is t=0 Choose the correct graph of f(x) and f below. Ов. OA AY 60- OD. o 60- 60- 604 0- O 10 10
4. (a) A function f has first derivative f' (x) - and second derivative f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative. 3 marks] (ii) Use the f'(x), and the First Derivative Test to classify each critical point. 3 marks (iii) Use the second derivative to examine...