Newton-Raphson: Sliding Down the Tangent Line

How does sliding down a tangent line beat halving at finding a square root — and why does it lead straight to functions?

Finger exercises

Short drills on what this video just taught. Write the code, run the checks, and reveal the answer only if you are stuck.

0 / 5 passed

Exercise 1 of 5

Evaluate the polynomial at a guess

Finding the square root of k means finding a root of f(x) = x**2 - k. To take a Newton step we first need f evaluated at the current guess. For k = 24 and a guess of 12, compute f(guess) and assign it to f_value.

(Hint: ** raises a number to a power.)

# Evaluate f(guess) = guess**2 - k, for k = 24 and guess = 12.
k = 24
guess = 12
f_value = ...  # your code here

# Evaluate f(guess) = guess**2 - k, for k = 24 and guess = 12.
k = 24
guess = 12
f_value = ...  # your code here

Python runs in your browser

⌘/Ctrl + Enter runs

is a number

evaluates the polynomial at the current guess

←Previous Fixing Bisection Search for Numbers Below One Next Abstraction and Decomposition: Why Your Phone Is a Black Box →