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Concept explainers
Given the formula
(a) Determine the maximum and the corresponding value of x for this function analytically (i.e., using
(b) Verify that Eq. (13.7) yields the same results based on initial guesses of
(a)
![Check Mark](/static/check-mark.png)
To calculate: The maximum value of the function and the corresponding value of variable
Answer to Problem 1P
Solution:
The maximum value of the function
Explanation of Solution
Given Information:
The function
Calculation:
Evaluate the first order derivative of the function
Equate equation (1) to zero and evaluate critical point.
Therefore, a critical point is at
Evaluate the second order derivative of the function
The sign of the second order derivative at
Substitute
Hence, the maximum value of the function at
(b)
![Check Mark](/static/check-mark.png)
To prove: The results obtained in part (a) using the equation as follows:
using the initial guess of
Explanation of Solution
Given Information:
The function is given as,
The initial guesses are
Formula used:
The expression for the parabolic interpolation is given as,
Here,
Proof:
Rewrite the equation of the parabolic interpolation:
Substitute
Thus, the value of
Substitute
Thus, the value of
Substitute
Thus, the value of
Substitute
Thus, the value of
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Chapter 13 Solutions
Numerical Methods for Engineers
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