If f (x) = x2-4x + 3, M = {(x, y) / F (x) + F (y) ≤ 0}, n = {(x, y) / F (x) - f (y) ≥ 0}, then the area of M, n is
Set M: (X-2) ^ 2 + (Y-2) ^ 2 = (Y-2) ^ 2, or (x + y-4) (X-Y) > = 0, two straight lines X + y-4 = 0 and X-Y = 0 divide m into four parts averagely, one of which is the intersection of M and N, so the area is 1 / 4 of the circle = pi / 2
RELATED INFORMATIONS
- 1. If the function f (x) = x2-4x + 3, the set M = {(x, y) | f (x) + F (y) ≤ 0}, and the set n = {(x, y) | f (x) - f (y) ≥ 0}, then the area of the region represented by the set M ∩ n in the plane rectangular coordinate system is______ .
- 2. Function f (x) = cos (3x + φ - π / 6) (0
- 3. If f (x) = cos (3x - α + π / 6) is odd, then Tan α is equal to
- 4. If f (x) satisfies f (x + 2) = f (x), f (2 + x) = f (2-x), and X belongs to [2,3], f (x) = (X-2) ^ 2, find the expression of F (x) in the interval [4,6]
- 5. Given that the function f (x) = X3 + MX2 + NX + 1 has extremum at x = two-thirds and x = 1, find the value of real number m, N and the monotone decreasing interval of function f (x) (...) Given that the function f (x) = X3 + MX2 + NX + 1 has extremum at x = two-thirds and x = 1, find the value of real number m, N and the monotone decreasing interval of function f (x) (necessary steps)
- 6. It is known that x = 1 is an extreme point of the function f (x) = mx3-3 (M + 1) x2 + NX + 1, where m, n ∈ R It is known that x = 1 is an extreme point of the function f (x) = mx3-3 (M + 1) x2 + NX + 1, where m, n ∈ R, M > 0 (1) Find the expression of the relationship between M and n; (2) Finding monotone interval of F (x); detailed process
- 7. It is known that x = 1 is an extreme point of the function f (x) = MX ^ 3-3 (M + 1) x ^ 2 + NX + 1
- 8. Given that the function f (x) = x ^ 3 + 3mx ^ 2 + NX + m ^ 2 has an extreme value of 0 when x = - 1, then M + n =? I will try 11 and 4, but the correct answer is only 11 Why give up 4?
- 9. If f (x) = ax ^ 3 + 3mx ^ 2 + NX + m ^ 2 has an extreme value of 0 when x = - 1, then M + n =? Note that the third power of X is preceded by A
- 10. Given that function x ^ 3 + 3mx ^ 2 + NX + m ^ 2 has extreme value 0 when x = - 1, find m and n
- 11. Given the function f (x) = x2 + 3x-2, what is f (2) = then
- 12. Given the function f (x-1) = x2-3x + 2, find f (x + 1)
- 13. Given the function f (2x + 1) = x2-3x + 2, find f (X-2)
- 14. Given the function f (x) = x2 + 3x + 1, then f (x + 1) is equal to
- 15. It is known that y = f (x) is an even function. When x > 0, f (x) = x + A / X (a > 0). When x is greater than or equal to - 3 and less than or equal to - 1, n ≤ f (x) ≤ m is constant 1) If a = 1, find the minimum of m-n 2) Finding the minimum value g (a) of M-N 3) When a > 16, is there K belonging to (1,2)], such that the inequality f (k-cosx) is greater than or equal to f (k ^ 2 - (cosx) ^ 2) belongs to R constant for any x? If so, find out the range of real number k; if not, explain the reason
- 16. It is known that y = f (x) is an even function. When x > 0, f (x) = (x-1) 2. If n ≤ f (x) ≤ m is constant when x ∈ [- 2, - 12], then the minimum value of M-N is () A. 13B. 12C. 34D. 1
- 17. If the maximum and minimum values of F (x) = x3-3x-a in the interval [0, 3] are m and N respectively, then the value of M-N is () A. 2B. 4C. 18D. 20
- 18. Given the function y = x & # 178; - 6x + 5. (1) the analytic expression is changed to the form of y = a (X-H) 178; + H;
- 19. Draw the following function image, and point out the symmetry axis, the maximum (minimum) value and the change of Y with X. 1, y = | - X & # 178; + 6x + 1|
- 20. The axis of symmetry of the parabola y = - X & # 178; - 6x is a straight line? The maximum value of the function is?