Interactive: Function and its first and second derivatives

# Plotting a function and its first and second derivatives in the Same Coordinate System # Lauri Ruotsalainen, 2010 @interact def func_deriv_interact( function = input_box(default=x^5-3*x^3+1, label="Function:"), x_range = input_box(default=(-2,2), label="Range (x)"), y_range = input_box(default=(-8,8), label="Range (y)") ): f(x) = function df(x) = derivative(f(x), x) ddf(x) = derivative(df(x), x) plots = plot(f(x), x_range, thickness=1.5) + plot(df(x), x_range, color="green") + plot(ddf(x), x_range, color="red") if y_range == (0,0): show(plots, xmin=x_range[0], xmax=x_range[1]) else: show(plots, xmin=x_range[0], xmax=x_range[1], ymin=y_range[0], ymax=y_range[1]) html("<center>$\color{Blue}{f(x) = %s}$</center>"%latex(f(x))) html("<center>$\color{Green}{f'(x) = %s}$</center>"%latex(df(x))) html("<center>$\color{Red}{f''(x) = %s}$</center>"%latex(ddf(x)))