Let f (x) = ax ^ 2 + BX (a ≠ 0) satisfy the condition 1. F (- 1 + x) = f (- 1-x); there is only one common point between the image of 2 function f (x) and the line y = X

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• 1. Given the quadratic function y = AX2 + BX + C, when the independent variable x takes X1 and X2, the function values are equal, then how to write the function when the independent variable x takes X1 + x2?
• 2. We know the function FX = x Λ 2 + 2x + 4, if X1 + x2 = 0 and X1 = 0
• 3. FX = ax ^ 2 + LNX if FX1 = (A-1 / 2) x ^ 2 + 2aX + (1-A ^ 2) LNX, FX2 = 1 / 2x ^ 2 + 2aX On (1, positive infinity), FX has FX1 in the common domain
• 4. Find the extremum of binary function f (x, y) = x ^ 2 + y ^ 3 + 4x-3y + 4, and explain whether it is a maximum or a minimum
• 5. How to judge whether the extreme point is a maximum or a minimum in the derivative function Such as the title
• 6. Finding the extremum of a given function f (x) = x-alnx (a ∈ R)
• 7. Given the function f (x) = alnx + 2 / x + X, 1, where a belongs to R. if a = 1, find the extreme point of F (x) 2. If f (x) increases in the interval [1, + infinity], find the value range of A
• 8. Let f (x) = X-2 / x-alnx. When a = 3, find the extremum of FX
• 9. For the cubic function f (x) = x ^ 3-3x ^ 2-3mx + 4 (M is a constant), the monotone interval of F (x) is obtained
• 10. Given the square of the algebraic formula x + ax + B, when x = - 1, its value is 5; when X-1, its value is - 1. Find the value of a and B
• 11. It is known that the quadratic function f (x) = ax ^ 2 + BX holds f (x minus 4) = f (2 minus x) for any x belonging to R, and the image of the function passes through a (1,3 / 2) (1) to find the function Given that the quadratic function f (x) = ax ^ 2 + BX belongs to R for any x, f (x minus 4) = f (2 minus x) holds, and the image of the function passes through a (1,3 / 2) (1) find the analytic expression of the function y = f (x) (2) if the solution set of the inequality f (x minus t) is less than or equal to x [4, M], find the value of the real number T, M
• 12. Given that the image of the function f (x) = AX3 + bx2 passes through the point m (1,4), the tangent of the curve at the point m is just perpendicular to the straight line x + 9y = 0. (1) find the value of real numbers a and B; (2) if the function f (x) monotonically increases in the interval [M, M + 1], find the value range of M
• 13. Let f (x) = AX2 + BX + C (a ≠ 0), y = f (x) pass through the point (0, 2A + 3), and the tangent at the point (- 1, f (- 1)) is perpendicular to the Y axis. (1) use a to represent B and C respectively; (2) when B · C reaches the minimum, find the monotone interval of the function g (x) = - f (x) · ex
• 14. Given the function f (x) = X3 + AX2 + BX + C, the tangent l of the curve y = f (x) at the point x = 1 is only the fourth quadrant, and the slope is 3, and the distance from the origin of the coordinate to the tangent L is 1010, if x = 23, y = f (x) has extremum. (1) find the value of a, B, C; (2) find the maximum and minimum value of y = f (x) on [- 3, 1]
• 15. Let f (x) = ax ^ 3 + BX + C (a is not equal to 0) be an odd function, the tangent of its image at point (1, f (1)) is perpendicular to the straight line x-6y-7 = 0, and the minimum value of derivative f '(x) is - 12 Ask for: 1) The value of a and B I want to ask what is the explanation for the lower tangent being perpendicular to the straight line x-6y-7 = 0? How can we calculate the slope of x-6y-7 = 0 to be 1 / 6? How can we get f '(1) = 3A + B = - 6? I don't quite understand these questions,
• 16. Let t not be equal to 0, and point P (T, 0) be a common point of the image of functions f (x) = x ^ 3 + ax and G (x) = BX ^ 2 + C. The images of two functions have the same tangent at point P 1. Denote a, B, C with T 2. If the function y = f (x) - G (x) monotonically decreases on (- 1,3), find the value range of T Please give us a detailed explanation,
• 17. F (x) = ax ^ 3 + BX + C (a is not equal to 0) is an odd function, the tangent of its image at (1, f (1)) is parallel to the straight line 6x + y + 7 = 0, and the minimum value of F '(x) is - 12 1. Find the value of a, B, C 2. Find the monotone increasing interval of function f (x), and find the maximum and minimum of function f (x) on [- 1,3]
• 18. If f (x) = ax ^ 2 + BX ^ 2 + C is even function, then f (x) = ax ^ 3 + BX ^ 2 + CX is even function Given that the function f (x) = ax ^ 2 + BX ^ 2 + C (a is not equal to zero) is even, then f (x) = ax ^ 3 + BX ^ 2 + CX is () A. Odd function B. even function C. both odd and even function D. non odd and non even function And why?
• 19. It is known that the function f (x) = x ^ 2-bx-3a + 6 is an even function, and its domain of definition is [a-2,2a + 1]. Find the range of (x) According to the past experience, a = x / 4, B = 3 / a (root x), there are 10000 yuan of capital invested in a and B, and 10000 yuan of capital invested in a and B. in order to obtain the maximum profit, we should pay more attention to the following aspects: 1, How many ten thousand yuan will be invested in each of the two commodities? What is the maximum profit?
• 20. If the even function f (x) is an increasing function in the interval [2,4] and the minimum value is 5, then f (x) is an increasing function in the interval [- 4, - 2]_ Function and is_ Maximum value