Phyton Function Graph

Question

Write a program that graphs a function of your choosing. Then select a point on that graph at which you want to estimate the derivative. The user can then choose a nearby point. The program will then show the graph of the function, as well as the line that connects your point and the user’s point. The program will also print out the slope of the line. In other words: • You might pick the function f(x) := x 3 − 2x + 1, and the point x = 2. • The program will tell the user what function it is (x 3 − 2x + 1) and what your chosen x-value is (x = 2). • The program will tell the user something like “Please choose a point to estimate the derivative at x = 2”. Say the user then inputs 2.1. • The program will graph y = f(x) and the line joining the points (2, f(2)) and (2.1, f(2.1)). • The program will then compute the slope of that line and print something like “The derivative is approximately (slope)”.

Frankly I have no idea how to do this.......

Answer 1

Let's tackle this one thing at a time and then combine them all at the end. It sounds like neither the choice of the function nor the choice of the point are part of the inputs, i.e., the function/point gets chosen before writing the program, and is not an option for the user.

1. Plot a graph of the function:

Use a graph plotting library if you don't want to reinvent the wheel here. A popular one is pylab. You probably also want to import numpy, both to have more freedom with what functions you can introduce and to make it easier to generate pairs of x/y values to plot. I'm going to choose as my function y = sin(x), and x = 1 as my point

import pylab

import numpy as np

x = np.linspace(0,2,100) #100 evenly spaced x-values between 0 and 2

y = np.sin(x) # y = sin(x) gives the y-values

pylab.plot(x,y) #plot the function

pylab.show() #show the plot

No interactivity yet, but we're getting there.

1. The user can choose a nearby point

We're going to need an input here. We should really make sure the input is a valid one, and not too far from 1 (or worse, not a real number at all). Since I don't know exactly how much you've learned about try/except blocks or exception handling yet, I'm going to just do the bare minimum here and just get an input:

a = float(input("Enter a decimal between 0 and 2, but not 1:"))

Putting the rest in is not too much work if you remember your algebra formulas:

import pylab

import numpy as np

x = np.linspace(0,2,100)

y = np.sin(x)

a = float(input("Enter a decimal between 0 and 2, but not 1:"))

b = np.sin(a)

m = (b - np.sin(1))/(a-1) #slope formula (y2 - y1)/(x2 - x1)

z = m*(x-1)+np.sin(1) # point-slope form for a line

pylab.plot(x,y)

pylab.plot(x,z)

pylab.show() #show can show multiple plots

print("The derivative of y = sin(x) at x = 1 is approximately",m)

The next step, if you want to improve this, would be to handle bad inputs the user might enter.