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The function f (x) = X3 + AX2 + BX + C, where a, B and C are real numbers. When a2-3b < 0, f (x) is () A. Increasing function B. decreasing function C. constant D. is neither increasing function nor decreasing function
If f ′ (x) = 3x2 + 2aX + B, where △ = 4a2-12b ＜ 0, f ′ (x) ＞ 0, then f (x) is an increasing function
It is known that there are two points a (x1, Y1) and B (X2, Y2) on the image with positive scale function y = KX. When x1y2, find the value of K
y1-y2=kx1-kx2=k(x1-x2)>0
Because x1-x2
As shown in the figure, the image of the linear function Y1 = KX + B and the image of the inverse scale function y2 = m / X intersect at two points a (2,1), B (1, - 2)?
The coordinates of B are (- 1, - 2) bar? 1, because a (2,1), B (- 1, - 2) are the points on Y1 = k x + B, then there are: 2K + B = 1, and - K + B = - 2.. solve this equation, get k = 1, B = - 1, so Y1 = X-1.. because a, B are the points on y2 = m / x, so m = 2, that is, y2 = 2 / X.2, from the figure, when - 1 < x < 0 or x > 2, Y1 > Y2
As shown in the figure, it is known that the image of the first-order function Y1 = KX + B and the inverse scale function y2 = MX intersect at points a (- 4, - 2) and B (2,4). (1) find the analytic expressions of these two functions; (2) answer according to the image, when x takes what value, Y1 > Y2?
(1) Substituting points a (- 4, - 2) and B (2,4) into Y1 = KX + B to get: - 4K + B = - 22K + B = 4, the solution is k = 1b = 2. Then the analytic formula of the first-order function is: Y1 = x + 2. Substituting B (2,4) into y2 = MX to get: M = 8, then the analytic formula of the inverse proportional function is: y2 = 8x; (2) when - 4 < x < 0 or x > 2, Y1 > Y2
RELATED INFORMATIONS
- 1. The image of the linear function Y1 = KX + B and the inverse scale function y2 = m / X intersect at two points a (- 2,1), B (1, n) 1) Find the expression of first-order function and inverse proportion function 2) Write Y1 > Y2
- 2. It is known that the quadratic function y = AX2 + BX + C (a ≠ 0) satisfies the following quantitative relationship between the independent variable x and the function value y X negative two thirds negative one negative half 0 half 1 half three Four fifths of Y minus two minus nine fourths of Y minus two minus five fourths of Y minus seven fourths of Y
- 3. It is known that in the quadratic function y = AX2 + BX + C, the corresponding values of function y and independent variable X are shown in the following table X - 3 - 20135 y 708 - 9 - 57 find the function value y when the symmetry axis X = 2 of y = ax + BX + C
- 4. If the point P (a, √ 3) is on the positive scale function y = - 3x, find the value of A
- 5. Y = (m-2) x to the power of M + 1 + 3x is a positive proportion function, and finding the relationship of positive proportion function is a formula
- 6. It is known that the quadratic function f (x) = ax Λ 2 + BX + 1 (a, B are constants, a ＞ 0) satisfies f (x-3) = f (1-x) and has the maximum value 4 in the interval ＜ - 3,2 ＞ find the value of a, B and find the range of the function f (x) in the interval ＜ - 3,2 ＞
- 7. The quadratic function f (x) = ax ^ 2 + BX + C satisfies the following conditions 1) F (- 1) = f (- 3); 2) f (x) has a minimum value of 3; 3) f (x) image passes through point (0,4), find the analytic expression of function f (x)
- 8. It is known that the left focus of the ellipse x ^ 2 + y ^ 2 / b ^ 2 = 1 (b belongs to (0,1)) is f, the left and right vertices are AC, the upper vertex is B, and the circle P is made through three points of FBC, where the coordinates of the center P are (m, n). Let f, B and C be (- C, 0), (0, b), (1,0) respectively. If the eccentricity of the ellipse e = 2 / 3, the equation of the circle P is obtained
- 9. It is known that the right focus a of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is the focus of parabola y ^ 2 = 8x, the vertex on the circle is B, and the eccentricity is √ 3 / 2,1, Find the path of ellipse C; 2, the line L passing through point (0, √ 2) with slope k intersects ellipse C at two points P and Q. if the abscissa of the midpoint of line PQ is 4 √ 2 / 5, find the equation of line L
- 10. The center of a circle is on the right focus of the ellipse 16x ^ 2 + 25y ^ 2 = 400, and passes through the vertex of the ellipse on the y-axis to find the equation of the circle
- 11. It is known that the minimum value of function f (x) = (2 ^ x-a) ^ 2 + (2 ^ - x-a) ^ 2 is 8, and there is a value range of real number a
- 12. It is known that a and B are real numbers, f (x) = x ^ 3 + ax, G (x) = x ^ 2 + BX, f '(x) and G' (x) are derivatives of F (x), G (x), if f '(x) g' (x) ≥ 0 in function area If f (x) and G (x) are monotonically consistent on interval I, then f (x) and G (x) are monotonically consistent on interval I 1. Let a > 0, if the monotonicity of functions f (x) and G (x) is consistent in the interval [- 1, + ∞), find the value range of real number B
- 13. Let the asymptote of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0) be tangent to the parabola y = x2 + 1, then the eccentricity of the hyperbola is equal to () A. 3B. 2C. 5D. 6
- 14. It is known that a focus of hyperbola C: x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0) is F2 (2,0) and B = root 3a. (1) the equation for solving hyperbola C (2) let a normal vector of line L passing through focus F2 be (m, 1). When line L and the right branch of hyperbola C intersect at two different points a and B, then, Find the value range of the real number m: and prove that the key point m of AB is on the curve 3 (x-1) ^ 2-y ^ 2 = 3. (3) let the right branch of the straight line L and the hyperbola C in (2) intersect at two points a and B. ask if there is a real number m, so that the angle AOB is an acute angle? If there is, find the range of M. if not, explain the reason
- 15. Polar coordinate equation 2 ρ cos ^ 2 θ / 2 = 5 is a circle B ellipse C hyperbola D parabola
- 16. Given that the polar equation of the parabola is ρ = 41 − cos θ, then the Quasilinear polar equation of the parabola is ρ = 41 − cos θ______ ．
- 17. If the polar coordinate equation of the curve is ρ & # 178; = 400 / (16cos & # 178; θ + 25sin & # 178; θ), the general equation of the curve is?
- 18. It is known that the parametric equation of C is x = 3cost y = 3sint (t is the parameter), and the tangent of C at point (0,3) is o If the origin of angular coordinate is the pole and the positive half axis of X axis is the polar axis, the polar coordinate equation of O is?
- 19. Elimination of parameters by parametric equation x=rθ-rsinθ y=r-rcosθ Elimination parameter θ nothing
- 20. Please talk about the method of solving the parametric equation by transforming triple integral, and the calculation method of curve and surface integral