The function f (x) = x3-x is known to decrease on (0, a) and increase on [a, + ∞). The value of a is obtained. The expert is requested to answer

From the meaning of the title, we know that the derivative of F (x) is 3x & # 178; - 1, so that it is equal to 0, and the solution is X & # 178; = 1 / 3
From the graph of F (x), we know that f (x) ′ = 3x & # 178; - 1 < 0 leads to - 1 / √ 3 < x < 1 / √ 3
F (x) = x3-x decreases on (0, a) and increases on [a, + ∞)
Then a = - 1 / √ 3

RELATED INFORMATIONS

1. If the function f (x) is an odd function defined on R and a decreasing function on the interval (negative infinity, 0), and f (x) = 0, then f (x)
2. Given that f (x) = X3 ax is a monotone increasing function on [1, + ∞), then the maximum value of a is______ ．
3. Given that a > 0, f (x) = - X3 + ax is a monotone decreasing function in [1, + ∞), then the maximum value of a is () A. 1B. 2C. 3D. 4
4. Given that a > 1, the function f (x) = the third power of X - ax is a monotone increasing function on [1, + infinity), then the maximum value of a is?
5. ---The problem of infinity and infinitesimal When X - > 0, is | x | / X infinite or infinitesimal? Please tell me why
6. On infinitesimal and infinity Is the function y = xcosx bounded from negative infinity to positive infinity? Is this function infinitesimal when x approaches positive infinity? Why?
7. What are the properties of infinity and infinitesimal?
8. Infinity - is infinity necessarily infinitesimal?
9. Learn the limit to tell the infinitesimal times infinity is equal to how much, why?
10. What is the result of infinitesimal multiplied by infinity? How to analyze this kind of problem?
11. Find the circumference of a circle with radius or diameter. Find the area of a circle with radius or diameter
12. How to get rid of brackets in mathematical algebraic expressions? How to change symbols? For example: - (A5 [power] - 6B) - (7 + 3b)
13. A sector with radius of 15 and center angle of 216 ° is rolled into the side of a cone, and the height and volume of the cone are calculated
14. What is the relationship between radius, linear velocity, angular velocity and period of a circle? And explain who decreases / increases with who increases
15. Put two squares with 5cm sides together to form a rectangle. What's the perimeter and area of the rectangle?
16. A simple harmonic motion with a period of 4S and an amplitude of 2cm is made. From t / 8 to t, the distance of the particle motion is smaller than 7cm. Why How about the journey of one eighth cycle? What do you mean by 6 + (2-2sin45)?
17. Cut the area of a circle into two sectors according to 2:7. The area of the large sector is 15 square centimeters more than that of the small sector. What is the area of the small sector?
18. What simple arithmetic does decimal multiplication have
19. A circle passes through a (- 2,1), B (5,0) and the center of the circle is on the straight line x-3y-10 = 0 A circle passes through a (- 2,1), B (5,0) and the center of the circle is on the straight line x-3y-10 = 0
20. Calculate the following questions with decimals 12m 9cm + 3M 48CM 6km - 4km 8m 2 yuan 54 Fen + 9Yuan 08 Fen