The graph of quadratic function f (x) = AX2 + BX + C (a ＞ B ＞ C) has two different intersections A and B with X axis, and f (1) = 0. ① find the range of C / A; ② prove that 3 / 2 ＜ ab ＜

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• 1. It is known that the quadratic function f (x) = AX2 + BX + C passes through points (0,1) and (1, - 5) and satisfies f (x) - f (- 2-x) 1, analytic expression of quadratic function 2, find the solution set of X when f (x) ≥ 0 That is to satisfy f (x) = f (- 2-x)
• 2. The instantaneous change rate of derivative is solved Which of you really understands derivative? High school derivative is just a simple concept, sometimes confusing. How can the instantaneous rate of change be determined, especially the derivative of X should be an approximate value, The derivative is a specific value. For example, when y = x ^ 2 + 2x is the derivative of x = 2, another point of the function image must be known. The value should be an ideal value by using the derivative formula. Because the derivative is the rate of change, all must be within the range of change, and here is to reduce the range of change to the minimum to get a specific value of a variable
• 3. Simple rate of change and derivative problem 1. Given the function y = x ^ 3-2, when x = 2, △ Y / △ x =? 2. Find the average change rate of y = x ^ 2-2x + 1 near x = - 2
• 4. Rate of change and derivative, help me look at this problem The average rate of change of function FX = the square of X + 3 near x = 1,2,3, which point has the smallest average rate of change? In detail, because I'm a bit stupid. What's the minimum value of instantaneous rate of change and what's the critical point?
• 5. Derivative, instantaneous rate of change When water is discharged from the water tank, the remaining water in the water tank after t minutes is Q (T) = 200 (30-t) ^ 2 (unit: liter). How fast does the water flow out just after 10 minutes? What is the average water flow out rate in the first 10 minutes?
• 6. Given the function f (x) = (A & # 178; + 4) e ^ (X-5), G (x) = (X & # 178; + ax-2a-3) e ^ (3-x) It is proved that when a ＜ - 6, there must be x1, X2 ∈ [0,5] such that f (x1) - G (x2) > 40
• 7. Within what is the function f (x) = x & # 178; - 4x + 3 a decreasing function
• 8. If the function f (x) = 2A & # 178; + (A-1) x + 3 is even, then a=
• 9. Let f (x) = 1 (x = 0) LG | x | (x ≠ 0) defined on R. if the equation F2 (x) + BF (x) + C = 0 has exactly three different real solutions x1, X2, X3, then X12 + X22 + X32=______ ．
• 10. Given the function f (x) = alnx - (1 + a) x + 0.5x ^ 2, (a belongs to R), if f (x) > = 0, it holds for any X in the domain of definition, and the value range of a is obtained
• 11. F (x) = root sign x g (x) = root sign (- x) to find the definition and range of function f (x) + G (x)
• 12. Given that the maximum value of function f (x) = - X & sup2; + 2aX + 1-A in the interval [0,1] is 2, find the value of real number a
• 13. Let f (x) = g (x) / x.1) find the value of a and B. 2) the inequality f (2 ^ x) - K2 ^ x > = 0 holds on [- 1,1]. 3) the equation f (| 2 ^ X-1 |) + K [(2 / | 2 ^ X-1 | - 3] = 0 has three different real number solutions and the range of K I don't know the third question
• 14. Let f (x) = g (x) / x.1) find the value of a and B. 2) the inequality f (2 ^ x) - K2 ^ x > = 0 holds on [- 1,1]. 3) the equation f (ABS (2 ^ x-1)) + K [(2 / ABS (2 ^ x-1)) - 3] = 0 has three different real number solutions and the range of K You'd better finish the problem
• 15. It is known that the function f (x) = 3x, f (a + 2) = 18, G (x) = λ· 3ax-4x has the semantic field of [0,1]. (I) find the value of a; (II) if the function g (x) is a monotone decreasing function in the interval [0,1], find the value range of real number λ
• 16. It is known that the odd function f (x) defined on [- 2,2] is a decreasing function. If f (1-2a) + F (A-1) < 0, the value range of a is obtained Such as the title
• 17. Given the function f (x) = log2 ((x-1) / (x + 1)), G (x) = 2aX + 1-A, and H (x) = f (x) + G (x) (1) the parity of H (x) is discussed; (2) when a = 1, it is proved that h (x) is monotonically increasing on X belonging to (1, + ∞), and that h (x) has two zeros; (3) if the equation f (x) = log2g (x) about X has two unequal real roots, find the value range of A
• 18. How many triangles are there if the sides of ABC are all integers and the maximum side is 4
• 19. The sides of △ ABC are all integers, and the maximum side is 7. How many triangles are there?
• 20. If the three variable lengths of a triangle are known to be three continuous natural numbers and the maximum angle is obtuse, then the lengths of the three sides are