x belongs to 0,2 , y x 8 what is the minimum of the square of 3x at this point x is 30

y=x(8-3x)^2

y'=(3x-8) 2+6x(3x-8)=(3x-8)(9x-8)x (0,2), x=8 9.

y''=9(3x-8)+3(9x-8)

x=8 9, y''=-48<0, where y has a maximum.

Because x (0,2) is a closed interval, the minimum cannot be calculated.

f(0)=0, f(2)=4, if the opening interval is the minimum value of 0

y=x under the root number multiplied by (8-3x) = under the root number (-3x 2+8x) = -3 under the root number (x 2-8 3x) = -3 under the root number [(x-4 3) 2-16 9] = under the root number [-3(x-4 3) 2+16 3]x belongs to (0,2) when x=4 3, y has a maximum value under the root number 16 3 = 4 3 * root number 3

y=x(64-48x+9x²)=9x³-48x²+64xy'=27x²-96x+64<0

3x-8)(9x-8)<0

8/90；8 9 So, when x = 8 9, y has a maximum value of 2048 81ps: the maximum value is correct

Find the axis of symmetry, draw an image with the image opening down, and look at the image.

Answer: xmax=4

Here's what I thought :

1.The difference between x and y should not be too bright, the smaller the difference between the two, the smaller the difference between the squares.

2.Then we limit that x and y are positive integers.

Then we can basically determine xmin=3 (x+y>3 through the skin, x=1 and 2 can be excluded).

In this case, y=1 does not meet the given conditions, then it can be determined that y=2, and x,y meet the conditions of the problem;

So let's move on.

x1=4,y1=3 compound question conditions; Respect the source.

x2=5,y2=4 does not meet the conditions of the question....

This gives xmax=4

y=（x-1）²-4

The image of the opener is upward, and the top spike point is (1,-4) and the function is monotonically decreasing in the range of x (-2,0), so when x=0, the minimum value is -3

And because x (-2,0), x cannot take the value of 0, so there is no minimum value.

Open interval, monotonically reduced, no maximum:

data-ik-caption-text="If it helps,"Good Yuyu > if it helps,

y=2x^2+3/x

2x 2 + Extreme X

More than and talk about the waiter shirt in 3 three times under the root number.

The minimum value is 3 times under the root number.

Since x 0 is called y 0, xy=8, then x+y 2 xy=4 hunger argument 2 (equal sign if and only if x=y).

So x+y+2 2+4 2, so the most balanced limb tease value of x+y+2 is 2+4 2

According to the basic inequality, we can get x+y 2 xy, so the minimum value of x+2+y is 2+2 8=2+4 2.

x+2) 2 Huai chain macro 4x=(x 2+4x+4) 4x=(x 2+4) 4x+1

Because x 2+4>=2sqrt(4x 2)=4x, (mean inequality calls filial piety) so (x 2+4) 4x>=1

So its minimum lead book value is 2

3x+12 x 2=>=3 times under the root number (multiply by 12 x 2) so the most ruined bush value = 3 times under the root number (27) = 3 at this time.

You need to know a formula: a+b> = 2 times the root of the hail under a*b, if and only if the lead a=b, the equal sign holds. The premise is that a and b are greater than zero;

Then 3x+12 x is greater than or equal to 2, and 3x * 12 x under the root number is 3x+12 x greater than or equal to 12

Don't forget to write the conclusion that the equal sign holds if and only if 3x=12 x, i.e. x=2.