This paper points out the monotone interval of the function f (x) = (x ^ 2 + 4x + 5) / (x ^ 2 + 4x + 4), and compares the magnitude of F (- π) and f (1)

This paper points out the monotone interval of the function f (x) = (x ^ 2 + 4x + 5) / (x ^ 2 + 4x + 4), and compares the magnitude of F (- π) and f (1)

f(x) = 1 + 1/(x+2)^2
It is equivalent to the function H (x) = 1 / x ^ 2 obtained by (- 2,1) translation
H (x) decreases monotonically at x0
So f (x) decreases monotonically when X-2
f(-π) = 1+1/(π-2)^2
f(1) = 1+1/9
Because (π - 2) ^ 2 < 9, f (- π) > F (- 1)

This paper points out the monotone interval of the function f (x) = the square of X + 4x + 5 / x + 4x + 4, and compares the size of F (- Pie) and f (- 2 / 2)

Note: ^ represents the second power, ^ ^ represents the third power
F (x) = [1 / (x + 2) ^] + 1, f '(x) = - 2 / (x + 2)^^
If f '(x) - 2, if f' (x) > O, we get X2 - (√ 2) / 2, so 1 / (π - 2)^

Finding monotone interval of function f (x) = x2-4x

A:
f(x)=x^2-4x
=(x^2-4x+2^2)-4
=(x-2)^2-4
The opening of parabola f (x) is upward, and the axis of symmetry x = 2
So:
The monotone decreasing interval is (- ∞, 2]
Monotone increasing interval is [2, + ∞)