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Given that the cube-12x + 8 of the function f (x) = x has the maximum and minimum values m and m respectively in the interval [- 3,3], then M-M = () It's like taking the derivation as an odd function, and then it won't work········
If f (x) = x ^ 3-12x + 8, it is impossible to find the maximum value in the specified interval
Let f '(x) = 0 find x, that is, the extreme point
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Let me help you
m=-8
M=24
M-m=32
F (x) = x3-27x, X belongs to [- 4,4]. Find the maximum and minimum of the function in a given interval
Let f * (x) = 3x ^ 2-27 = 0, the solution is: X1 = - 3, X2 = 3
Furthermore, f (- 4) = - 4 * (- 11) = 44, f (- 3) = - 3 * (- 18) = 54, f (3) = - 54, f (4) = - 44
The maximum and minimum values of the function in the given interval are 54 and - 54 respectively
In the following linear function, y decreases with the increase of X, and ()
A. y=3xB. y=3x-2C. y=3+2xD. y=-3x-2
∵ in the first-order function y = KX + B, when k > 0, y increases with the increase of X; when k < 0, y decreases with the increase of X. the first-order functions of a, B and C all increase with the increase of X; the first-order function of d y = - 3x - 2, y decreases with the increase of X
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- 1. The image of a certain function passes through the point (- 1,2), and the value of function y decreases with the increase of independent variable x. please write a function relation that meets the above conditions___ ．
- 2. 1. Positive scale function y = 1 / 2x_____ The value of quadrant y decreases with the decrease of X_____ 2. If the image with positive scale function y = KX (k is not equal to 0) passes through the point (1 / 3, - 1 / 2), then the image passes through the point______ Quadrant, K=______ 23. If the image with positive scale function y = x / m-2 passes through the second and fourth quadrants, the value range of M is________
- 3. I have two questions. 1. Do odd functions have f (0) = 0? Why? two Given function f (x) has f (y + x) = f (x) + 2Y (x + y) for any real number x, y Cut f (1) = 1, find the analytic expression of F (x) That's what I did F（1+Y）=F（1）+2Y（1+Y） Let 1 + y = T. replace y = T-1 Replace the above formula to get 2T square - 2T = 1 But the answer is 2x squared - 1 What's wrong with me, I know algebra, but why not?
- 4. "Mathematics function of senior one" asks all senior brothers and sisters to answer [if f (x) = x2 + BX + C, and f (1) = 0, f (3) = 0, find the value of F (- 1)] Note: 2 refers to the square
- 5. Function equation f (x) - 2F (- x) = x ^ 2-5x, find f (x) The solution given by the answer is to construct another equation f (- x) + 2F (x) = x ^ 2 + 5x, but I don't know the basis of such construction?
- 6. Find the definition field (1) f (x) = loga (1 + 3x-4x ^ 2) (a > 1 and a ≠ 1); (2) f (x) = [LG (2x ^ 2 + 5x-12)] / √ (x ^ 2-3)
- 7. Let f (x) = 2mcos ^ 2x-2 √ 3msinx * cosx + n (M > 0) be defined as [0, Pai / 2] range [1,4] (1) (2) if f (x) = 2, find X
- 8. Let f (x) be a quadratic function, and f (x-1) + F (2x + 1) = 5x ^ 2 + 2x, find f (x)
- 9. It is known that f (x) = x & sup2; - (K-2) x + K & sup2; + 3K + 5 has two zeros if the two zeros of the function are α and β, Find the value range of α & # 178; + β & # 178
- 10. Given the function f (x) = (k ^ 2 + 1) x ^ 2-2kx - (k-1) ^ 2 (K ∈ R), X1 and X2 are the two zeros of F (x), and X1 > x2（ Given the function f (x) = (k ^ 2 + 1) x ^ 2-2kx - (k-1) ^ 2 (K ∈ R), X1 and X2 are the two zeros of F (x), and X1 > x2 (1) (I) prove: X1 = 1; (II) find the value range of x2; (2) Let g (k) be the minimum value of function f (x). When x 2 ∈ [- 2, - 1], find the maximum value of G (k)
- 11. It is known that the maximum value of the function f (x) = a ^ x (a > 0, and a ≠ 1) in the interval [1,2] is m, and the minimum value is n 1, if M + n = 6, find the value of real number a If M = 2n, find the value of real number a Wait online
- 12. If f (x) = - x ^ 2 + 2aX and G (x) = (a + 1) ^ (1-x) are decreasing functions in the interval [1,2], find a
- 13. If the function f (x) = SiNx + | SiNx |, X ∈ [0,2 π] has only two different intersections with the line y = k, then the value range of K is
- 14. If f (x) = SiNx + 2 | SiNx | (x ∈ [0,2 π)] and y = k have only two different intersections, then the value range of K is () A. [-1，1]B. （1，3）C. （-1，0）∪（0，3）D. [1，3]
- 15. Given the function f (x) = (SiNx cosx) SiNx, X belongs to R 1. Change it into the form of asin (Wx + a) + B. 2. Find the period
- 16. Find the following function analytic formula (1) known f (x + 1) = x & # 178; - 3x + 2 find f (x) (2) known f ((radical x) + 1) = 2 + 2 (radical) x find f (x)
- 17. It is proved that the function f (x) = 2 / 2 of X is an increasing function on (- infinity, 0)
- 18. It is known that the image of quadratic function y = ax & # - 178; + BX + C passes through point a (1,0) B (2, - 3) C (0,5) 1. Find the analytic expression of this quadratic function 2. The vertex coordinates of the quadratic function are obtained by the collocation method
- 19. Quadratic function f (x) = ax & # 178; + BX + C For any x ∈ R, is there a, B, C ∈ R, which satisfies that ① f (x-1) + F (- 1-x) = 0 and f (x) ≥ 0, and ② 0 ≤ f (x) - x It should be that there are 0 ≤ f (x) - x ≤ 1 / 2 (x-1) &;
- 20. If the minimum value of quadratic function y = x & # 178; - MX + 3 is - 3, then M=