The most difficult mathematical function

f(5-x^2)=(5-x^2)^2+2(5-x^2)- 1=g(x)

The derivative of this function is: g' (x) = 2 (5-x 2) (-2x)-4x = 4x (x 2-6) = 4x (x+6 (1/2)) (x-6 (1/2))

Discussion: In 4 consecutive time intervals:

1.(- infinity, -6 (1/2)],

g '(x)& lt； 0,

Function monotonically decreases.

2.x=-6^( 1/2),g'(x)=0

Minimum value.

3.(-6^( 1/2),0]

g′(x)>0,

Function monotonically increases.

4.x=0, g'(x)=0 maximum.

5.(0,6^( 1/2)]

g '(x)& lt； 0,

Function monotonically decreases.

6.x = 6 (1/2), and g' (x) = 0 minimum.

7.(6 (1/2), positive infinity], g'(x)>0,

Function monotonically increases.