325-This program runs an interactive grapher. Given a function, it will try to compute the first and second derivatives, the plot t.sagews

This program runs an interactive grapher. Given a function, it will try to compute the first and second derivatives, the plot them in different colors.

This first cell contains an example of what will be done with the interactive grapher.

# Example
f(x) = x*(x+3)*(x-1)*(x-3)^2
Xmin = -4
Xmax = 4

# Set up the derivatives of the given function        
df(x) = derivative(f(x))
d2f(x) = derivative(df(x))

# Set Range
Ymin = min(min(f.find_minimum_on_interval(Xmin,Xmax)), min(df.find_minimum_on_interval(Xmin,Xmax)), min(d2f.find_minimum_on_interval(Xmin,Xmax)))
Ymax = max(max(f.find_maximum_on_interval(Xmin,Xmax)), max(df.find_maximum_on_interval(Xmin,Xmax)), max(d2f.find_maximum_on_interval(Xmin,Xmax)))  

# Set up the graphs of the function and derivatives
P = plot(f, Xmin, Xmax)    
P = P + plot(df, Xmin, Xmax, color = 'red')    
P = P + plot(d2f, Xmin, Xmax, color = 'green') 

# Graph it all
html("Original function in blue, 1st derivative in red, 2nd derivative in green")
show(P, Xmin, Xmax, Ymin, Ymax )

Original function in blue, 1st derivative in red, 2nd derivative in green

Interactive Grapher

@interact
def _(f = input_box(default=x, label = 'Function:'), Xmin = input_box(default=-10, label = 'xmin:'), Xmax = input_box(default=10, label = 'xmax:')): 

    # Set up the derivatives of the given function        
    df(x) = derivative(f(x))
    d2f(x) = derivative(df(x))

    # Set Range
    Ymin = min(min(f.find_minimum_on_interval(Xmin,Xmax)), min(df.find_minimum_on_interval(Xmin,Xmax)), min(d2f.find_minimum_on_interval(Xmin,Xmax)))
    Ymax = max(max(f.find_maximum_on_interval(Xmin,Xmax)), max(df.find_maximum_on_interval(Xmin,Xmax)), max(d2f.find_maximum_on_interval(Xmin,Xmax)))
    
    # Set up the graphs of the function and derivatives
    P = plot(f, Xmin, Xmax)    
    P = P + plot(df, Xmin, Xmax, color = 'red')    
    P = P + plot(d2f, Xmin, Xmax, color = 'green') 

    # Graph it all
    html("Original function in blue, 1st derivative in red, 2nd derivative in green")
    show(P, Xmin, Xmax, Ymin, Ymax )