Find the maximum and minimum values of the function f = x | x + 4 | in the interval [1, a]

Find the maximum and minimum values of the function f = x | x + 4 | in the interval [1, a]

The interval [1, a] satisfies x > - 4, so the square of F = x + 4x increases monotonically on [1, a], so the minimum value
F (1) = 5 maximum f (a) = the square of a + 4A

Calculation | x2-9 | ≤ x + 3

The left side of the inequality is the absolute value term, which is constant and nonnegative, so x + 3 ≥ 0, X ≥ - 3
|x^2-9|≤x+3
-x-3≤x^2-9≤x+3
x^2-9≤x+3
x^2-x-12≤0
(x-4)(x+3)≤0
-3≤x≤4
x^2-9≥-x-3
x^2+x-6≥0
(x+3)(x-2)≥0
X ≥ 2 or X ≤ - 3
In conclusion, x = - 3 or 2 ≤ x ≤ 4

(X-2) (x2-6x-9) - x (X-5) (x-3) where x = - 1 / 3

As a result, we will be able to find the following formula: x-6x-\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(- 15x = - 12x = - 12 * (- 1 / 3) = 4

1 + x2 + x2 + x2 + 1 + x2 + 4 + x2 + 9 = (x + 1 + 1 + X + 1 + 1 + 1) (x + 1 + 1 + X + 1) how to calculate x
How to solve the equation 1 + x2 + x2 + x2 + 1 + x2 + 4 + x2 + 9 = (x + 1 + 1 + X + 1 + 1 + 1) (x + 1 + 1 + X + 1)

5x²+15=(2x+5)(2x+3)
5x²+15=4x²+16x+15
x²-16x=0
x(x-16)=0
∴x1=0 x2=16