Find the necessary and sufficient condition that all the images of the function f (x) = (M2 + 4m-5) x2-4 (m-1) x + 3 are above the x-axis M ＜ 1 or m ＞ 4 1 ≤ m ＜ 19, the intersection should be 4 ≤ m ＜ 19, why not

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• 1. Given that the function f (x) = the third power of 1 / 3 * x + the square of M * x, where m is a real number, (1) the tangent slope of function FX at X-1 is 1 / 3, find the value of M, find the process
• 2. Given that the increasing function of function f (x) = x to the second power-2ax-3 is [1, + ∞), then the value of real number a is
• 3. How to judge the monotonicity of function with derivative
• 4. Using function derivative to judge function monotonicity It is known that: in general, if f '(x) is zero at a finite number of points in an interval and is positive (or negative) at the other points, then f (x) is still monotonically increasing (or decreasing) in the interval. Correct. Is it correct if f' (x) does not exist at a finite number of points in an interval?
• 5. If the derivatives of F (x) on the left and right sides of x0 are different, is x0 the extreme point of F (x)
• 6. Derivative f '(x) is the extreme value of F (x) at x = x0. What does x in x = x0 mean? Does it mean a specific number or a variable?
• 7. When Lagrange multiplier method is used to find the extremum of multivariate function, if the solution of partial derivative equal to zero is vector x0, can we use Hessian matrix to determine whether point x0 is the extremum of function?
• 8. The derivative of the negative half power of the function y = 3x at point x0 = is equal to
• 9. The derivative of a function at a given point: for example, y = x square, x0 = 2
• 10. In a hurry Using derivative to solve the problem of monotone interval greater than or equal to 0 Which is greater than or equal to 0 and which is greater than or equal to 0 when the derivative is used to calculate the monotone increasing interval and the value range when an interval is increasing? Why? If the monotone interval is greater than or equal to 0, then the single increasing and single decreasing interval does not have to use the closed interval
• 11. Given the function f (x) = x2-4, if f (- m2-m-1) < f (3), then the value range of real number m is () A. （-2，2）B. （-1，2）C. （-2，1）D. （-1，1）
• 12. The even function f (x) defined on R satisfies that for any x 1, x 2 belongs to [0, positive infinity] (x 1 ≠ x 2), if (f (x 2) - f (x 1)) / (x 2-x 1), then () A.f(3)＜f（-2）＜f（1） B.f(1）＜f(-2)＜f(3) C.f(-2)＜f(1)＜f(3) D.f(3)＜f(1)＜f(-2）
• 13. If the even function f (x) defined on R has f (x2) - f (x2) / x2-x1 < 0 for any X1 x2 ∈ [0, + ∞) (x1 is not equal to x2), then a f (3) < f (- 2) < f (1) B F (1) < f (- 2) < f (3) C f (- 2) < f (1) < f (3) d f (3) < f (1) < f (- 2)
• 14. Find the maximum and minimum value of the function y = - 2Sin (x + π / 6) + 3 in the following interval and the corresponding value of X (1) r, (2) [0, π] (3) [π / 2, π / 2]
• 15. Find the maximum and minimum values of the function g (x) = 2Sin (x - π / 3) in the interval [0, π] Such as the title
• 16. Find the period, monotone interval, maximum and minimum of the function y = 2Sin (π / 3x-2 / 5 π x), and take the maximum and minimum The set of values of X.
• 17. 3. Given that the minimum value of function f (x) = 2sinwx in the interval [- 60 degrees, 45 degrees] is - 2, then the value range of W is? Our teacher gave us two formulas 60 degrees > t / 4 45 degrees > t / 4 T=2π/w But I don't know who can explain
• 18. The function f (x) is known to satisfy f (a + b) = f (a) + F (b) - 6 for any real number a, B ∈ R. when a > 0, f (a)
• 19. Let f (x) be a function defined on R, if f (0) = 2010, and for any x ∈ R, f (x + 2) - f (x) ≤ 3.2X, f (x + 6) - f (x) ≥ 63.2x, then f (2010)=______ ．
• 20. Let x 1x 2 be a quadratic equation of one variable with respect to X. x (square) - 2 (m-1) x + m + 1 = 0. Two real roots are obtained. Y = x 1 + x 2 (both have squares). The analytic trial and range of y = f (m) are obtained