> 一阶导数描述函数的单调性和极值

The first derivation described whether the `y` of that function should increasing or decreasing:

First decreasing, then increasing, you'll get a minimum

First increasing, then decreasing, you'll get a maximum

Increasing intervals 递增区间

Decreasing intervals 递减区间

    import numpy as np
    from scipy.misc import derivative

    # define a function
    def f(x):
        return x**2

    # define x range
    unit = 0.1
    input_x = np.arange(-2, 2 + unit, unit)

    # find what x make f prime of x equle 0
    whole_derivative = [(index, derivative(f, x, dx=1e-6)) for index, x in enumerate(input_x)]
    x_of_zero_derivative = [input_x[index] for index, d in whole_derivative if abs(d) < 0.1]
    the_x = x_of_zero_derivative[len(x_of_zero_derivative)//2]

    # get each side derivative of the_x
    left_x = the_x - 1
    right_x = the_x + 1
    left_derivative = derivative(f, left_x, dx=1e-6)
    right_derivative = derivative(f, right_x, dx=1e-6)

    # do a conclution
    if left_derivative < 0:
        print('from negative infinite to 0, the function is decreasing')
    if right_derivative > 0:
        print('from 0 to positive infinite, the function is increasing')
    if left_derivative < 0 and right_derivative > 0:
        print('the f({x})={y} is the mininum of x**2'.format(x=int(the_x), y=f(int(the_x))))

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