Concept explainers
a.
To find the intervals on which the function is increasing by using analytical method.
a.
Answer to Problem 14RE
The function
Explanation of Solution
Given:
The function is
Calculation:
The function
Now put
Below is graph
Therefore ,the critical points are
So , there are three intervals that is
put
put
put
Therefore , the function is increasing in interval
Below is the graph of
From graph of
b.
To find the intervals on which the function is decreasing by using analytical method.
b.
Answer to Problem 14RE
The function is decreasing in interval is
Explanation of Solution
Given:
The function is
Calculation:
The function
Now put
Below is graph
Therefore ,the critical points are
So , there are three intervals that is
put
put
put
Therefore , the function is decreasing in interval is
Below is the graph of
From graph of
c.
To find the intervals on which the function is concave up by using analytical method.
c.
Answer to Problem 14RE
The Function
Explanation of Solution
Given:
The function is
Calculation:
The graph of a twice differentiable function
Concave up on any interval where
Since,
First derivative :
Second derivative :
Now, put
Therefore , there are two intervals that is
check the value of
Now for
Now for
Therefore, the Function
Below is the graph of
From graph it is clear that, the Function
d.
To find the intervals on which the function is concave down by using analytical method.
d.
Answer to Problem 14RE
The Function
Explanation of Solution
Given:
The function is
Calculation:
The graph of a twice differentiable function
Concave up on any interval where
Since,
First derivative :
Second derivative :
Now, put
Therefore , there are two intervals that is
check the value of
Now for
Now for
Therefore, the Function
Below is the graph of
From graph it is clear that, the Function
e.
To find any local extreme values.
e.
Answer to Problem 14RE
The function
Explanation of Solution
Given:
The function is
Calculation:
Graph of
From graph it is clear that the function
f.
To find inflections points.
f.
Answer to Problem 14RE
The inflection point is at
Explanation of Solution
Given:
The function is
Calculation:
Inflection point of any function is a point where the graph of function has a tangent line and where the concavity changes.
Since,
Therefore, the inflection point is at
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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