Our objective is to develop a Python program that analyzes quadratic functions, computes their derivatives, identifies critical points (minima and maxima), and visualizes these functions in a clear and informative way. Additionally, we’ll calculate the area under the curve for a complete analysis.
- Derivative Calculation: We started by writing a dynamic function that calculates the derivative of any given function with respect to x. The function is flexible enough to take an input function f(x) and return its derivative.
- Test the Derivative Function: We defined a complex equation with at least two minima and two maxima. Using this equation, we tested the derivative function from the first step to verify that it works correctly.
- Visualizing the Equation: We used Matplotlib to visualize the equation. The graph shows the behavior of the function, including the minima and maxima points.
- Identifying Minima and Maxima: After plotting, we created arrays to store the x-values of the minima and maxima points. We then printed these arrays to display the critical points and ensure our calculations are accurate.
- Global Minima and Maxima: We computed the global minima and maxima of the equation. Once computed, we printed their coordinates to identify the overall minimum and maximum values of the function.
- Visualizing Global Minima and Maxima: On our graph, we added clear and distinguishable markers to highlight the global minima and maxima. This will ensure that these critical points are easily identifiable on the plot.
- Finding the Area Under the Curve: We implemented a method to compute the area under the curve of the equation to enhance the overall analysis.
- Python 3.x
- numpy for handling mathematical and numeric operations.
- sympy for symbolic mathematics and derivative calculations.
- matplotlib for plotting the graphs.
- Abimbola Ronald
- Justice Chukwuonye
- Jordan Nguepi
- Eunice Adewusi
- Glen Miracle