def cubic_derivative_approximation(f, t0, t1):
f0 = f(t0)
f1 = f(t1)
diff_f = f.derivative()
d0 = diff_f(t0)
d1 = diff_f(t1)
return CubicSpline.endpoint_slope_factory(t0, t1, f0, f1, d0, d1)
def linear_approximation(f, t0, t1):
f0 = f(t0)
f1 = f(t1)
slope = (f1-f0)/(t1-t0)
return CubicSpline.endpoint_slope_factory(t0, t1, f0, f1, slope, slope)
