Consider the following graph of the function y=f(x)
M201-more practice with concepts
1. Consider the following graph of the function y=f(x)
[pic]
Use this graph to answer the following questions.
____________Where is f(x) continuous but not differentiable?
____________Where does f(x) have a jump discontinuity?
____________List f’(-1), f’(1), and f’(3) in increasing order.
____________What is [pic]f(x) ?
____________ What is [pic]f(x) ?
____________ What is [pic]f(x) ?
____________ What is [pic]f(x) ?
2. Using the graph of f(x) given above, sketch a graph of [pic].
3. Sketch a graph that meets the following nine conditions:
[pic] [pic] does not exist f is continuous on (0, infinity)
[pic] [pic] [pic] f(12)= -1
[pic] on (-infinity, 0), (0,5), (12,20) [pic] on (5,12)
4. Is it possible to sketch a graph of a function f(x) that is…
a) continuous everywhere but not differentiable at x=2
b) differentiable everywhere but not continuous at x=2
c) continuous on [-3,7], f(-3)=-2, f(7)=10 but f(x) has no roots
d) continuous on [-3,7], f(-3)=10, f(7)= 0 but f(x) [pic]2 anywhere on [-3,7]
e) always increasing except at x=0, where f’(0)=0
f) always concave down and always increasing
5. Given the graphs of f(x), g(x) find ( use graph on page 272, #68)
a) [pic] if h(x)= f(g(x))
b) [pic] if [pic]
c) [pic] if [pic]
d) [pic]if [pic]
6. Given the curve of f(x) below, answer the questions listed below.
Use graph that is on page 362, #18
a) If you were to make a good initial guess x1 to find the root at 2 using Newton’s Method , what intervals could x lie in?
b) If you were to make a good initial guess x1 to find the root at -2 using Newton’s Method , what intervals could x lie in?
c) If you were to make a good initial guess x1 to find the root at 4 using Newton’s Method , what intervals could x lie in?
d) Suppose you make and initial guess of x1=5.5 using Newton’s Method, what would happen?
e) Suppose you make and initial guess of x1=2.5 using Newton’s Method. On the graph above apply Newton’s Method to find x2 and x3.
7. The derivative of f(x) is shown in the graph below.
Use graph that is on page 362, #18
a) When is f(x) increasing?
b) What are the local maximum and minimum of f(x)?
c) When is f(x) concave up?
8. The velocity of an object is shown in the below graph.
Use the graph on page 304, #8
a) When is the object moving forward?
b) When is the object slowing down?
c) At what time(s) does the object reach its maximum position?
9. What does the Mean Value Theorem say about f(x) (shown below) on the interval….
(Use the graph on page 304, #2)
a) [ 0,5]?
b) [3,6]?
c) [0,4]?
10. Sketch the graph of [pic], given the graph of f(x) below.
(Use the graph on page 304, #2)
12. Sketch a possible graph of f(x), given the graph of [pic] below.
Use the graph on page 304 #8
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