Calculates the maximum and minimum values of a cubic curve.
Author: shiroeExecutions: 926
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Let the form of a cubic function be y = ax³ + bx² + cx + d.
Enter the coefficients a, b, c, and the constant term c. Also,
enter the lower bound L (the minimum value x can take) of the domain,
and the upper bound R (the maximum value x can take) of the domain.
Enter a non-zero value for a. If 0 is entered, it will be converted to 1.
Enter a value for L that is less than R.
Enter different values for L and R.
If the same value is entered for both L and R, the selected values will be
adjusted.
After the calculation is performed, each “selected value” will be displayed.
Please refer to each “selected value” and double-check your input.
The program will output the maximum and minimum values of the cubic function
within the range defined by the domain.
The rest is for reference only.
Enter the coefficients a, b, c, and the constant term c. Also,
enter the lower bound L (the minimum value x can take) of the domain,
and the upper bound R (the maximum value x can take) of the domain.
Enter a non-zero value for a. If 0 is entered, it will be converted to 1.
Enter a value for L that is less than R.
Enter different values for L and R.
If the same value is entered for both L and R, the selected values will be
adjusted.
After the calculation is performed, each “selected value” will be displayed.
Please refer to each “selected value” and double-check your input.
The program will output the maximum and minimum values of the cubic function
within the range defined by the domain.
The rest is for reference only.
| The adopted value for a | |
| The value adopted for b | |
| Adopted values for c | |
| d's adopted value | |
| Adopted values for L | |
| R's Adopted Values | |
| Maximum value | |
| Minimum value | |
| Discriminant | Discriminant for first-derivative-equal-to-zero conditions |
| f(L) | |
| f(R) | |
| f(α) | |
| f(β) | |
| α | Solutions to the first derivative f'(x) = (the smaller one). |
| β | Solutions to the first derivative f'(x) = (the larger one). |
| The coefficient of the first derivative is 3a | |
| Coefficient 2b of the first derivative | |
| The constant term c in the first derivative | |
| The coefficient of the second derivative, 6a | |
| Constant term 2b of the second derivative | |
| The numerical value of -b/3a | Values of x for which the second derivative equals 0 |
| Y-coordinate of the inflection point | f''(-b/3a) = 0, the value of f(-b/3a) |
| Presence or Absence of Duplicate Maximum Values | Duplicate maximum values: 1 (present), 0 (absent) |
| Presence or Absence of Duplicate Minimum Values | Duplicate minimum values: 1 (present), 0 (absent) |
R5 (2023). Dec. 28 (th)_“Calculating Maxima and Minima of Cubic Curves”
ver.test_001
50keta
ver.test_001
50keta
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For a cubic function with a domain that is a closed interval, this function
calculates the maximum and minimum values of the cubic function within its range of values.