Determine the monotone interval and extremum of the function y = x ^ (1 / 3) * (1-x) ^ (2 / 3)

Determine the monotone interval and extremum of the function y = x ^ (1 / 3) * (1-x) ^ (2 / 3)

Y = x ^ (1 / 3) * (1-x) ^ (2 / 3) = [x (1-x) ^ 2] ^ (1 / 3) = [x ^ 3-2x ^ 2 + x] ^ (1 / 3) y '= (1 / 3) (3x ^ 2-4x + 1) * (x ^ 3-2x ^ 2 + x) ^ (- 2 / 3) = (1 / 3) (3x ^ 2-4x + 1) * [(x ^ 3-2x ^ 2 + x) ^ 2] ^ (- 1 / 3) [(x ^ 3-2x ^ 2 + x) ^ 2] ^ (- 1 / 3) > = 03x ^ 2-4x + 1 = (3x-1) (x-1) X1 y' > - 0 monotone increasing

How to find the monotone interval and extremum of function y = x + 1 / X

This is the check function. The image is as follows:
Increasing intervals (- ∞, - 1) and (1, + ∞)
Minus intervals & nbsp; (- 1,0) and (0,1)

U = {1,2,3,4,5,6}, a = {2,3,5}, B = {1,4}. Cu (a ∪ b) and (CUA) ∩ (cub)

(A∪B)={1,2,3,4,5,}
∪ Cu (a ∪ b) = &; (empty set)
(CUA) ∩ (cub) = Cu (a ∪ b) = &; (empty set)
(CUA) ∩ (cub) = Cu (a ∪ b) this is an equation

As shown in the figure, in RT △ ABC, ab = AC, ∠ BAC = 90 °, ∠ 1 = ∠ 2, CE ⊥ BD is extended to E. verification: BD = 2ce

It is proved that: extend the intersection of CE and BA at point F, as shown in the figure, ∵ be ⊥ EC, ∵ bef = ∠ CEB = 90 °. ∵ BD bisection ∵ ABC, ∵ 1 = ∠ 2, ∵ f = ∠ BCF, ∵ BF = BC, ∵ be ⊥ CF, ∵ CE = 12CF, ∵ △ ABC, AC = AB, ∵ a = 90 °, ∵ CBA = 45 ° and ∵ f = (180-45) ° △ 2 = 67.5 °

Find the area of the figure enclosed by the parabola y = x & # 178; and Y & # 178; = X

I'm glad to answer your question
Solving equations
y=x^2
y^2=x,
The intersection points (0,0) and (1,1) of the curves are obtained
What is the area of the figure enclosed by the curve
∫【0,1】(√x-x^2)dx
=[(2/3)x^(3/2)-x^3/3]│【0,1】
=2/3-1/3
=1/3

∫ (x ^ 7 / (x ^ 4 + 2)) DX, indefinite integral

Answer: ∫ [x ^ 7 / (x ^ 4 + 2)] DX
=∫[(x^4)*(x^3)/(x^4+2)]dx
=(1/4)∫[(x^4+2-2)/(x^4+2)]d(x^4+2)
=(1/4)∫[1-2/(x^4+2)]d(x^4+2)
=(x^4+2)/4-(1/2)ln(x^4+2)+C1
=(x^4)/4-(1/2)ln(x^4+2)+C

A mathematical problem "arithmetic required"
There are 27 boxes of pens and pencils, a total of 300. There are 10 pens in each box and 12 pencils in each box. How many boxes of pens and pencils are there?
Rolling of the equation

Pen: (27 * 12-300) / (12-10) = 12 (box)
Pencil: 27-12 = 15 (box)

The parallelogram rule means that the force is added at the beginning and end, that is, f = F1 + F2 + F3 +

The triangle rule is that multiple vectors are connected end to end. Looking at the beginning of the first vector and the end of the last vector, it is the sum of vectors
The rule of parallelogram is that the heads of two vectors intersect at a point, and then make a complete parallelogram according to the direction and size of the two vectors. The intersection of the heads and the diagonal points of the parallelogram form the vector sum
In fact, when two vectors are added, the two rules are equivalent. You can use either one. When the vectors exceed two, the triangle rule is more convenient

（1）140+150+160+170+180
=（ ）*（ ）
=（ ）

The average of these three numbers is 160, so
160 * 5=800

The vertex of isosceles triangle is a (4,2), and the bottom end is B (3,5). Find the trajectory equation of the other vertex C, and explain what its trajectory is?

∵A（4，2），B （3，5）∴|AB|=10… (2 points) ∵ the vertex of an isosceles triangle is a, and the end point of its bottom is B, C | Ca | = 10, that is, C is on a circle with a center and a radius of 10 The equation is (x-4) 2 + (Y-2) 2 = 10 So the trajectory equation is (x-4) 2 + (Y-2) 2 = 10 (x ≠ 3,5) In order to improve the students' ability of analyzing and solving problems, we should take a (4,2) as the center of the circle, and take a 10 as the radius of the circle to remove (3,5) and (5, - 1) (14 points)