Exercise 14.3#
Question 1#
The roots of the function \(f(x) = e^x - 1\) can be found mathematically (without the use of numercial methods).
Plot \(f(x)\) on an interval containing the root.
Without using a root finding method from a package, write a function for the bisection method that takes
\(f\) (and \(f'\) where relevant)
the initial guess
the tolerance/precision
as arguments.
Verify your function by using it to find the root. Test a few values for the initial guess, what if you pick the value of the root?
Hint:
Functions are like any other Python object and can be set as the value of a variable or argument.
Question 2#
The function \(f(x) = e^x - 3 x - 4\) has two roots inside of the interval \([-2, 3]\).
Plot \(f(x)\) over the given interval and take note of roughly where these roots lie.
Find each of these roots using the function you defined in Question 1. Plot a curve for \(f(x)\) and dots where you have found the roots.