(a.)
To Show:
(a.)
Answer to Problem 59E
It has been shown that
Explanation of Solution
Given:
The average flow velocity
Concept used:
A function attains maximum value at a point where its first derivative is zero and its second derivative is negative.
Calculation:
It is given that
Simplifying,
Differentiating with respect to
Simplifying,
Differentiating again with respect to
Equating the first derivative to zero,
This implies that either
Now, it is given that
So,
Then, the only feasible solution is
Put
Simplifying,
On further simplification,
Note that the above quantity is negative because
This shows that
Conclusion:
It has been shown that
(b.)
The graph of
(b.)
Answer to Problem 59E
The graph of
Explanation of Solution
Given:
The average flow velocity
Concept used:
A function attains maximum value at a point where its first derivative is zero and its second derivative is negative.
Calculation:
It is given that
Put
The graph of this function over the interval
As shown previously,
Put
It can be seen from the graph that in the given case,
Conclusion:
The graph of
Chapter 4 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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