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?

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• 1. 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?
• 2. The derivative of the negative half power of the function y = 3x at point x0 = is equal to
• 3. The derivative of a function at a given point: for example, y = x square, x0 = 2
• 4. 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
• 5. It is proved that the derivative of monotone function is not necessarily monotone function
• 6. It is said in the mathematics book that the derivative is greater than 0 and the function increases monotonically. I think that no matter what the case is, first the derivative is greater than or equal to 0, and then exclude the case that the derivative is in a section or constant to 0 (when the original function is parallel to the X axis, it is not tenable). Therefore, I think what is said in the book is not accurate,
• 7. Why the first derivative of a function is always greater than 0 can not deduce the monotonic increasing of the function Our postgraduate entrance examination teacher said that if the first derivative is greater than 0, we can deduce the monotone function, but we can't deduce the increasing or decreasing function, which is different from what I learned before
• 8. ）To find the derivative, = (a ^ x) / (a ^ x-1) = 1 + 1 / (a ^ x-1) because a ^ X-1 > 0 is constant, so the derivative is greater than 0, and the function increases monotonously. I don't understand the derivative
• 9. Functions with derivatives less than 0 are monotone increasing A right B wrong
• 10. The relationship between monotone increasing function and derivative?
• 11. If the derivatives of F (x) on the left and right sides of x0 are different, is x0 the extreme point of F (x)
• 12. 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?
• 13. How to judge the monotonicity of function with derivative
• 14. 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
• 15. 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
• 16. 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
• 17. 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）
• 18. 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）
• 19. 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)
• 20. 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]