1. Suppose that y = f(x) is a continuous function defined on the interval 0, E(0 E). Below is a graph of f'(x), the derivative of f(x), which is defined atall points of 0, E except at x =}С.0А!С:EDA graph of f'(), where it is defineda. Where is f (x) increasing or decreasing? Where does f (x) have points oflocal extrema in (0, E)? (Reminder: local extrema cannot occur at endpoints)b. Where is f(x) concave up or concave down? Where does f(x) haveinflection points?Draw a possible graph of f(x) which uses all information given andс.deduced about f(x).B

Question
Asked Nov 8, 2019

Question 1 Parts A, B, and C

1. Suppose that y = f(x) is a continuous function defined on the interval 0, E
(0 E). Below is a graph of f'(x), the derivative of f(x), which is defined at
all points of 0, E except at x =
}
С.
0
А!
С:
E
D
A graph of f'(), where it is defined
a. Where is f (x) increasing or decreasing? Where does f (x) have points of
local extrema in (0, E)? (Reminder: local extrema cannot occur at endpoints)
b. Where is f(x) concave up or concave down? Where does f(x) have
inflection points?
Draw a possible graph of f(x) which uses all information given and
с.
deduced about f(x).
B
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1. Suppose that y = f(x) is a continuous function defined on the interval 0, E (0 E). Below is a graph of f'(x), the derivative of f(x), which is defined at all points of 0, E except at x = } С. 0 А! С: E D A graph of f'(), where it is defined a. Where is f (x) increasing or decreasing? Where does f (x) have points of local extrema in (0, E)? (Reminder: local extrema cannot occur at endpoints) b. Where is f(x) concave up or concave down? Where does f(x) have inflection points? Draw a possible graph of f(x) which uses all information given and с. deduced about f(x). B

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Step 1

Consider the given graph.

The function fx) is increases when f'(x)>0
From the graph it is observed that f'(x)>0 in the interval (0,C)U(D,E)
Hence, the function is increasing in the above interval.
The function fx) is decreases when f (x)<0
From the graph it is observed that f'(x)<0 in the interval (C,D)
The function has local extreme value where f'(x)=0
The function has local extreme value at x = B and D
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The function fx) is increases when f'(x)>0 From the graph it is observed that f'(x)>0 in the interval (0,C)U(D,E) Hence, the function is increasing in the above interval. The function fx) is decreases when f (x)<0 From the graph it is observed that f'(x)<0 in the interval (C,D) The function has local extreme value where f'(x)=0 The function has local extreme value at x = B and D

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Step 2

(b)

...
The function is concave up when f"(x)>0 or f'(x) is increasing.
From the graph if is observed that the function is concave up in the interval
(0,A)U(B,C)U (C,E)
The function is concave down in the interval (A, B)
Inflection point occurs when f"(x)=0
From the graph It is observed that the function has inflection point at
x A andx C.
Hence, the function is continuous function but the function is undefined at x = C.
help_outline

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The function is concave up when f"(x)>0 or f'(x) is increasing. From the graph if is observed that the function is concave up in the interval (0,A)U(B,C)U (C,E) The function is concave down in the interval (A, B) Inflection point occurs when f"(x)=0 From the graph It is observed that the function has inflection point at x A andx C. Hence, the function is continuous function but the function is undefined at x = C.

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