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The cost function of a monopoly firm with constant cost is AC = MC = 10 and the market demand function is q = 60-p. (1) find the equilibrium output, price and profit; (2) If the demand function is q = 45-0.5p, find the equilibrium output, price and profit at this time; (3) If the demand function is q = 100-2p, find the equilibrium output, price and profit at this time; (4) This explains why there is no monopoly supply curve
1) First find the MR function: P = 60-q, r = 60q-q ^ 2, Mr = 60-2q
When Mr = MC, 10 = 60-2q, q = 25, P = 35, profit = (35-10) * 25 = 625
2) P = 90-2q, r = 90q-2q ^ 2, Mr = 90-4q, when Mr = MC, 10 = 90-4q, q = 20, P = 50
Profit = (50-10) * 20 = 800
3) P = 50-q / 2, r = 50q-q ^ 2 / 2, Mr = 50-q, when Mr = MC, 10 = 50-q, q = 40, P = 30
Profit = (30-10) * 40 = 400
4) The supply curve we usually call is a supply curve derived by solving the problem of profit maximization under constraints
Monopoly firms face a given demand curve and have only one supply point, so monopoly firms have no supply curve
Given that a is not equal to 0, find the definition field of function f (x) = root 2 [1 + LG (A-X) - LG (a + x)]
According to the logarithm, the number should be greater than 0, including: A-X > 0; a+x>0
If a > 0, - A
Let the function f (x) = {|lg|x-1|, X is not equal to 1, x = 1} if the equation f (x) ^ 2 + BF (x) + C = 0 Let the function f (x) = {LG | X-1 |, X is not equal to 1, x = 1} if the equation f (x) ^ 2 + BF (x) + C = 0 has and only has three different roots x1x2x3, then X1 + x2 + X3=
Drawing to analyze
1, f (x) image is axisymmetric about x = 1,
2. The equation has three roots. Make a straight line y = B on the f (x) image so that it has three intersections with the f (x) image, so make two straight lines, that is
b1=0,b2>0,
3. Find the sum of the X values of the three intersections of the line y = B and the f (x) image, that is, one root is 1, and the other two are about 1 pair
Call. And 3
The functions f (x) = 2lg (x + 1) and G (x) = LG (2x + T) (t is a constant) are known (1) Find the definition domain of function f (x); (2) If x ∈ [0,1], G (x) is meaningful, find the value range of real number t (3) If f (x) ≤ g (x) is constant when x ∈ [0,1], find the value range of real number t
(1) When x + 1 > 0, i.e. x > - 1 ≠ the definition domain of function f (x) is (- 1, + ∞) (2) ∵ x ∈ [0,1], G (x) is meaningful ∵ 2x + T > 0 is constant on [0,1], i.e. when t > 0 ∵ the value range of real number T is (0, + ∞) (3) ∵ x ∈ [0,1], f (x) ≤ g (x) is constant
The function whose domain is {x| Xer and X is not equal to 0} is: y = 1 / SiNx, y = x2 / 3, y = lg| X|
It's not easy, y = lg|x|
Because the real number must be greater than 0, but the absolute value symbol is added! X can be any real number except 0!
It is known that the function y = a ^ LG (3-ax) (a > 0, a is not equal to 1) is the range of subtracting function to find a in its definition field [- 1,1]
3-ax is a subtractive function
Y = a ^ LG (3-ax) is a subtractive function in its domain [- 1,1]
Then a > 1
Consider domain
3-ax>0 ax0 x1
a
RELATED INFORMATIONS
- 1. Let a > 0 and a ≠ 1, then the inverse function of function y = logax and function y = loga1 The image of the inverse function of X (about) A. X-axis symmetry B. Y-axis symmetry C. Y = x symmetry D. Origin symmetry
- 2. The function f (x) defined on a positive real number belongs to a positive real number for any m and N, and f (MN) = f (m) + F (n) holds. When x > 1, f (x) < 0. It is proved that f (x) is a subtractive function on a positive real number
- 3. . f (x) is an odd function over the definition field R and satisfies f (x + 2) = f (x). When x belongs to (0,1). F (x) = 2 ^ X-1, find f (log2 / 1 6
- 4. For the function y = f (x) with domain D, if the following conditions are met at the same time 1. F (x) monotonically increases or decreases in D. 2. The value range on the existence interval [a, b] is [a, b], and f (x) is called a closed function 1. Find the interval where the closed function y = - x ^ 3 meets condition 2. 2. Judge whether f (x) = (3 / 4) x + 1 / X (x is greater than 0) is a closed function and explain the reason. 3. Judge whether the function y = K + root sign (x + 2) is a closed function. If so, find the value range of K
- 5. The definition domain of function f (x) is D, if: 1. F (x) is a monotone function in D; If [a, b] belongs to D, so that the value range of F (x) on [a, b] is [a, b], then y = f (x) is called a closed function. Now f (x) = K + radical x + 2 is a closed function, then the range of K is?
- 6. If the domain of function y = f (x) is [0,3], then the domain of function g (x) = (f (x + 1)) / (X-2) is
- 7. Find the primary function f (x) so that f [f (x)] = 9x + 1
- 8. It is known that f (x) is an even function, which is a subtractive function on [0, + ∞). If f (lgx) > F (1), the value range of X is
- 9. Quadratic function y = ax ²+ The image of K (a ≠ 0) passes through points a (1, - 1), B (2,5),,, urgent,,, urgent Quadratic function y = ax ²+ The image of K (a ≠ 0) passes through points a (1, - 1), B (2,5) (1) Find the expression of the function 2. If point C (- 2, m) (n, 7) is also in the function image, find the value of M, n 3. Is point E (2,6) on this image? Why?
- 10. Quadratic function f (x) = ax ²+ The coefficients a, B and C of BX + C are not equal to each other. If 1 / A, 1 / B and 1 / C form an equal difference sequence, a, C and B form an equal ratio sequence, and the maximum value of F (x) on [- 1,0] is - 6, then a= Hope to have a detailed answer. Thank you
- 11. It is known that the definition domain of function f (x) is x ∈ [- 1] 2，3 2] , find g (x) = f (AX) + F (x a) (a > 0)
- 12. The even function f (x) defined on R is a subtractive function on [0, + ∞), and f (1 / 2) = 0. Then the value range of X with F [Log1 / 4 (x)] > 0 is satisfied
- 13. Example 4. It is known that the function y = f (x) is a periodic function defined on R, the period T = 5, and the function y = f (x) (- 1 ≤ x ≤ 1) is an odd function. It is also known that y = f (x) is a primary function on [0,1], a quadratic function on [1,4], and the minimum value of the function is - 5 when x = 2 ① It is proved that f (1) + F (4) = 0; ② Find the analytical formula of y = f (x), X ∈ [1,4]; ③ Find the analytical formula of y = f (x) on [4,9]
- 14. On the maximum value of trigonometric function Just explain how the formula changes Y = maximum value of sinxcosx + cosx + SiNx If it's right, I can add another 50 points Don't use the universal formula. Can you do it with double angle?
- 15. A small problem in trigonometric function of senior one mathematics (for finding value range) Known function f (x) = [6 × The fourth power of cosx + 5 × Square - 4] / cos2x of SiNx, find its range Talk about your ideas, (you'd better attach the answer) sin ² We haven't learned the conversion of x = (1-cos2x) / 2. Can you tell me why it is so converted?
- 16. If the domain of functions f (x) = 3 ^ x + 3 ^ - X and 9 (x) = 3x-3 ^ - x is r, then a, f (x) and 9 (x) are even functions, B, f (x) are even functions, and 9 (x) If the domain of functions f (x) = 3 ^ x + 3 ^ - X and 9 (x) = 3x-3 ^ - x is r, then A, f (x) and 9 (x) are even functions B F (x) is an even function and 9 (x) is an odd function C, f (x) and 9 (x) are odd functions D f (x) is an odd function and 9 (x) is an even function
- 17. The even function f (x) defined on R monotonically increases in the interval (0, + infinity), and f (2a square + A + 1)
- 18. The function y = f (x) is an even function on R and an increasing function on (- ∞, 0]. If f (a) ≤ f (2), the value range of real number a is () A. a≤2 B. a≥-2 C. -2≤a≤2 D. A ≤ - 2 or a ≥ 2
- 19. It is known that f (x) is a function defined on the real number set R and satisfies f (x + 2) - f (x + 2) f (x) - f (x) = 6, f (1) = - 1 / 2, f (2) = - 1 / 4, then f (2006) =?
- 20. It is known that f (x) is an odd function defined on the real number set R, and when x ∈ (0,1), f (x) = 2 ^ X / (4 ^ x + 1) 1. Find the analytical formula of function f (x) on [- 1,1] 2. Judge the monotonicity of F (x) on (0,1) and prove it 3. When t takes what value, the equation f (x) = t has a real number solution on [- 1,1]