Tags:Derivative Tangent Line Slope Python

Finding Horizontal Tangent Lines in Python

Author: David Manuel

In this video, it is shown how to use Python to find any horizontal tangent lines for a function. The presenter finds the derivative of the function in Python and then has Python solve when the derivative is equal to zero. This equation is solved numerically by giving Python a starting guess for the solution, which was found from a graph of the function.

Transcript 13

Exercises

Python Code: 
from sympy import *

x=symbols('x')
y=(6*x**2-4*x**3)/(2*sqrt(x**3*(2-x)))

Python Code: 
matplotlib notebook

plot(y,(x,0,2),ylim=[-10,10])

dy=diff(y,x).simplify()
print(dy)

horiz=nsolve(dy,x,0.75)
print('The graph has a horizontal tangent line at x=',horiz)

Open Python Notebook File