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1. The monotone interval of function y = x ^ 4-4x ^ 2-5 is? 1. Find the monotone interval and extremum of function y = x ^ 3-x ^ 2-x + 1? I want to explain, because the foundation is not very good, many do not understand
① Because y = x ^ 4-4x ^ 2-5, so y '= 4x ^ 3-8x, let y' = 4x ^ 3-8x = 0 get: x = 0 or ± root 2. From the list, we can see that the monotone increasing intervals of y = x ^ 4-4x ^ 2-5 are: (- root 2,0) and (root 2, + infinity), and the monotone decreasing intervals of Y are: (- infinity, - root 2) and
(0, root 2)
② Because y = x ^ 3-x ^ 2-x + 1, so y '= 3x ^ 2-2x-1, let y' = 3x ^ 2-2x-1 = 0 get: x = 1 or - 1 / 3, the list shows that the monotone increasing interval of y = x ^ 3-x ^ 2-x + 1 is: (- infinite, - 1 / 3) and (1, + infinite), and the monotone decreasing interval of Y is: (- 1 / 3,1), so
Y gets the maximum at x = - 1 / 3: y = f (- 1 / 3) = 32 / 27, y gets the minimum at x = 1: y = f (1) = 0
In the plane coordinate system, O is the coordinate origin, take a point P on the image of the function y = – 3x, pass through the point P as the PA ⊥ X axis, the abscissa of the known point P is – 2, and calculate the area of the triangle POA
Take - 2 into y = - 3x to get PA = 6, and then solve it according to the triangle area formula, that is, s = 1 / 2PA × OA
Take a point P on the image of the function y = - 3, and make the PA ⊥ X axis through the P point. Given that the coordinate of P point is - 2, it is necessary to find the area of △ POA (o is the origin of the coordinate)
Because PA = 3, Ao = 2, this is a right triangle, PA Ao is a right side, so s = PA * AO * 1 / 2 = 3
Let f (x) be continuous in the closed interval [0.1] and differentiable in [0.1], f (0) = 0, f (1) = 1. It is proved that there exists ξ ε (0,1) such that f (ξ) + F '(ξ) = 0
F (1) = 0. Constructor f (x) = f (x) e ^ x, Rolle theorem, f '(ξ) = 0. Simplification is the answer
To do the mixed operation of addition and subtraction of rational numbers, we first unify the subtraction into method, and then use the sum of method to carry out the operation, that is, a + B-C = a + B + (- C)
To do the mixed operation of addition and subtraction of rational numbers, first the subtraction is unified into addition, and then the operation is carried out by using the commutative law and associative law of addition, i.e. a + B-C = a + B + (- C)
Given a = (5 √ 3cosx, cosx), B = (SiNx, 2cosx), Let f (x) = a · B + | B | ^ 2-1 / 2
1. When - π / 6 ≤ x ≤ π / 4, find the range of function f (x)
2. In (1), when the function f (x) is the maximum, we find the minimum value of | 2A / t-tb | (t ∈ R and t ≠ 0)
F (x) = AB + | B | ^ 2-1 / 2 = 5 √ 3cosxsinx + 2 (cosx) ^ 2 + (SiNx) ^ 2 + 4 (cosx) ^ 2-1 / 2 = (5 √ 3 / 2) sin2x + 6 (1 + cos2x) / 2 + (1-cos2x) / 2-1 / 2 = (5 √ 3 / 2) sin2x + (5 / 2) cos2x + 3 = 5sin (2x + π / 6) + 3 - π / 6 ≤ x ≤ π / 4, - π / 6 ≤ 2x + π / 6 ≤ 2 π / 3 F (x) in 2
What is abdication addition and subtraction
31-8 = 13
Subtraction starts from the low, 1 minus 8, if not enough, borrow 1 from the ten, that is, a ten, so that 11-8 = 3
At this time, the 3 on the 10th bit becomes 2, that is, the 3 on the original 10th bit takes out 1 and retreats to one bit to participate in the calculation. In this way, the 10th bit is 2, so 31-8 = 23, which is abdication minus
Given that the solutions X and y of the equations 2x + y = a + 1, x-2y = 3a-2 are positive numbers, then the value range of a is?
Solve the equations {2x + y = a + 1, x-2y = 3a-2
The solution is: {x = a, y = 1-A
∵ X and y are positive numbers
∴a>0,1-a>0
∴0
In the case of 123456789 nine numbers, the formula is established. One four digit number multiplied by one digit equals another four digit number. The number can not be repeated
1738 * 4 = 6952
1963 * 4 = 7852
A of right angle △ AOB is the intersection of hyperbola y = K / X and straight line y = - X - (K + 1) in the second quadrant. Ab ⊥ X axis is in B, and △ AOB area is 3 / 2
(1) If there are two intersections A and C between the straight line and the hyperbola, and the abscissa of a and the ordinate of C are - 1, the coordinates of a and C and the area of △ AOC can be obtained. O is the coordinate origin
1) K / x = - X - (K + 1) x ^ 2 + (K + 1) x + k = 0 (x + 1) (x + k) = 0x1 = - 1, X2 = - K is in the second quadrant, so the abscissa of K0, a is X1 = - 1, ordinate = K / - 1 = - Ka (- 1, - K) B (- 1,0) △ AOB area = AB * Bo / 2 = k * 1 / 2 = K / 2, and △ AOB area = 3 / 2, so K / 2 = 3 / 2K = 3. These two functions are: y = 3 / xy = - X -
RELATED INFORMATIONS
- 1. Take a point P on the image of the function y = - 3x, pass through the point P and make PA perpendicular to the X axis. Given that the abscissa of the point P is - 2, find the area of the triangle POA of the triangle and help me Take a point P on the graph of function y = - 3x, pass through point P to make PA perpendicular to X axis, the abscissa of known point P is - 2, find the area of triangle POA of triangle, who can help me
- 2. Given that the image of the function y = | x2-1 | / X-1 has exactly two intersections with the image of the function y = KX, then the value range of K is? I just want to know if the range of K can go to 2
- 3. For the function f (x), if there exists x0 ∈ r such that f (x0) = x0 holds, then x0 is called the fixed point of F (x) For the function f (x), if there exists x0 ∈ r such that f (x0) = x0 holds, then x0 is called the fixed point of F (x), if f (x) = x ^ 2 + A / (bx-c) (B, C ∈ n +) There are only two fixed points 0,2, and f (- 2)
- 4. Let a set a = [0,1], B = [1,2], piecewise function f (x) = 2 ^ x, (x belongs to a); f (x) = 4-2x, (x belongs to b). If x0 belongs to a, and f [f (x0)] belongs to a, then what is the value range of x0. The answer is (log is the logarithm of 3 / 2 at the bottom of 2, 1) I hope to explain the process in detail,
- 5. Given the function f (x) = sin (2wx - π / 6) (W > 0), for any m belonging to R, the image of function y = f (x) (x belonging to [M, M + π]) and the line y = 1 have only one intersection, then w =?
- 6. The function f (x) = ax + B, a, B ∈ R, when x is greater than or equal to - 1 and less than or equal to 1, the absolute value of F (x) is less than or equal to 1 It is proved that the absolute values of a and B are less than or equal to 1
- 7. Given the function f (x) = x ^ 3 + BX + CX + 2, the extremum is obtained at x = 2 / 3 Determine the analytic expression of function f (x) and find the monotone interval of function f (x)
- 8. Given that the two extreme points of the function f (x) = ax ^ 3 + BX ^ 2 + CX + D are - 1 and 3, and f (0) = - 7, f '(0) = - 18, find the expression of F (x)
- 9. If the odd function f (x) = ax ^ 3 + (B-1) x ^ 2 + CX has an extreme value at x = 1, then 3A + B + C=
- 10. Let min {x, y} denote the minimum value of X and y, for example, min {0,2} = 0, min {12,8} = 8, then the function y of X Let min {x, y} denote the minimum value of X and y, for example, min {0,2} = 0, min {12,8} = 8, then the function y of X can be expressed as ()
- 11. Determine the monotone interval and extremum of the function y = x ^ (1 / 3) * (1-x) ^ (2 / 3)
- 12. Finding the maximum value of the function y = x ^ 2-3x + 2 in the interval [1 / 2,2]
- 13. If x is known to be greater than 0 and less than 2 / 3, then the maximum value of the function y = x (2-3x) is? Don't copy it
- 14. Given x > 0, the maximum value of function y = 2-3x-4 / x?
- 15. Let f (x) = - 1 / 3x ^ 3 + ax have three monotone intervals, then the value range of a is
- 16. Derivative function of F (x) = 3x-2 / x + 3 I totally forget that I am f (x) = 3-11 / x + 3 = 11 / (x + 3) * 2
- 17. Given that the function f (x) = x3-ax2 + 2ax-1 is an increasing function in the interval (1, + ∞), find the value range of real number a?
- 18. What is the symmetry of the image of the function f (x) = (1 / x) + SiNx
- 19. What is the minimum value of the function f (x) = - x + 3x + 4 Wrong. What is the minimum value of F (x) = - x ^ 3 + 3x + 4
- 20. The extremum of the function y = x-e Λ x is?