Question 1#

The roots of the function $f(x)=e^x-1$ can be found mathematically (without the use of numercial methods).

1. Plot $f(x)$ on an interval containing the root.

2. Without using a root finding method from a package, write a function for the bisection method that takes

   • $f$

   • the initial interval

   • the tolerance/precision

   as arguments.

   Verify your function by using it to find the root. Test a few values for the initial interval, 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 $f(x)=e^x-3x-4$ has two roots inside of the interval $[-2,3]$.

1. Plot $f(x)$ over the given interval and take note of roughly where these roots lie.

2. 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.