# Math Help - Inequalities. (1)

1. ## Inequalities. (1)

Let x&y be real numbers such that : $-2 \leq x \leq 1$ and $1 \leq 3x-x^2+2y^2 \leq 22$

Show that : $-4 \leq y \leq 4$

2. I would start by letting $f(x)=3x-x^{2},$ and finding its extremes on the interval $[-2,1].$ What do you get?

3. Finding extremes is a method in calculus.
This is pre-calculus subforum.

4. -2<x<1

-6<3x<3

0<x^2<1

-6<3x-x^2<2

5. Originally Posted by TWiX
Finding extremes is a method in calculus.
You have a parabola, so you can do it with basic algebra.

6. Originally Posted by Also sprach Zarathustra
-2<x<1

-6<3x<3

0<x^2<1

-6<3x-x^2<2
I think there is an error here. The correct inequality is

$-10\le 3x-x^{2}\le 2.$

Do you see how to get this?