import numpy as np
import matplotlib.pyplot as plt
plt.close()

eps=10**(-7)

def myFunct(x):
    return(np.sin(x)+x**2/50+x/4)

def myFunctDerivative(x):
    return(np.cos(x)+x/25+1/4)

def plotDerivative(x):
    dx=1
    m=myFunctDerivative(x)
    dy=m
    y=myFunct(x)
#    plt.plot([x-dx, x, x+dx],[y-dy, y, y+dy])
    plt.plot(x,y,'md')
    plt.plot([x-dx, x],[y-dy, y])

x=np.arange(-10,10,.1)
y=myFunct(x)
plt.plot(x,y)
plt.grid(True)

x0=1.5

y0=myFunct(x0)
plotDerivative(x0)

c=.3
eps=10**(-4)

grad=myFunctDerivative(x0)

while np.abs(grad)>eps:
    x0=x0-c*grad
    plotDerivative(x0)
    plt.plot([x0],[0],'.r')
    grad=myFunctDerivative(x0)