Homework 2 Worksheet.ipynb

Kernel: SageMath (stable)

f(x) = e^sin(x)^3 + x^6-2*x^4-x^3-1
fd(x) = derivative(f(x),x)
fdd(x) = derivative(fd(x),x)

grx = plot(f(x),(x,-2,2), color = 'red')
grx+= plot(fd(x),(x,-2,2), color = 'green')
grx+= plot(fdd(x),(x,-2,2), color = 'blue')
show(grx)

x = 1.530134
fd(x)

14.9727759326443

x = 0
fd(x)
fdd(x)
fddd= derivative(fdd(x),x)
fdddd = derivative(fddd)
fddddd = derivative(fdddd)

def multiplicity(f,a):
    i = 0
    while (f(x=a) != 0):
        f(x) = derivative(f(a),x)
        i = i + 1
        multiplicity(f(x),a)
f(x) = x^2-1        
multiplicity(f,0)