The derivative value of the differentiable function y = f (x) at one point is 0, which is the extreme value of the function y = f (x) at this point () A. Sufficient condition B. necessary condition C. necessary and insufficient condition D. sufficient and necessary condition

For the differentiable function f (x) = X3, f '(x) = 3x2, f' (0) = 0, we can't deduce that f (x) takes the extremum at x = 0, so when the derivative is 0, we don't necessarily take the extremum. For any function, when the differentiable function takes the extremum at a certain point, the derivative at this point must be 0. So we should choose & nbsp; C

RELATED INFORMATIONS

1. If y = f (x) is a differentiable function and f '(1) = 2, then when x = - 1, the derivative value of function f (- x) is the solution
2. The function f (x) = AX3 + 3x2 + 2, if f '(- 1) = 4, then the value of a is equal to______ ．
3. If the sum of function value and derivative value of function f (x) = xlnx at x0 is equal to 1, then the value of x0 is equal to 1______ ．
4. Why is the derivative of y = f (x) = x equal to 1 and the derivative of y = f (x) = C equal to 0 Ask the teacher to explain to me clearly, I almost fainted
5. Y = g (x + at) + F (X-AT), it is proved that the second derivative of Y for t is equal to a ^ 2 times of the second derivative of Y for X
6. If the derivative of F (x) = (x-3) (X-6) (X-9) is not obtained, it shows that the derivative of equation f (x) is equal to zero and has several real roots
7. If f (x) = (x-1) (X-2) (x-3) (x-4), how many real roots does the derivative of the equation have? If f (x) = (x-1) (X-2) (x-3) (x-4), how many real roots does the derivative of the equation have I don't know how to determine the image between 1 and 2, 2 and 3, 3 and 4. I feel that there is at least one between them, not one
8. If f (0) = 0, f ′ (0) = a, then limf (x) / X is in X → 0=
9. Limf (x) = a (x → x0), if f (x) > 0, is there a > 0?
10. F (x) is invertible in positive and negative infinity, and limf '(x) = e, Lim [(x + C) / (x-C)] ^ x = Lim [f (x) - f (x-1)], find C when x →∞ The answer in my book is: Lagrange mean value theorem and the second important limit formula! The final answer is C = 1 / 2
11. The derivative value of the differentiable function y = f (x) at one point is 0, which is the extreme value of the function y = f (x) at this point () A. Sufficient condition B. necessary condition C. necessary and insufficient condition D. sufficient and necessary condition
12. The derivative value of the differentiable function y = f (x) at one point is 0, which is the extreme value of the function y = f (x) at this point () A. Sufficient condition B. necessary condition C. necessary and insufficient condition D. sufficient and necessary condition
13. Given that the function y = FX defined on R satisfies f (2 + x) = 3f (x), when x ∈ [0,2], f (x) = x-2x, find f (x) when x ∈ [- 4, - 2]=
14. Let f (x) = {X-1, X ≥ 1, x, - 1
15. If f (x) = 2x + 1 and X is not equal to 1, find limf (x) (x tends to 1) and prove it by using ε - δ I don't know much about this
16. F (0) = f (1) = 0, f (1 / 2) = 1. It is proved that there is at least one point in (0,1) such that f '(x) = 1 F (x) is continuous on [0,1] and differentiable in (0,1).
17. Why is the proposition "when limx →∞ f (x) = 0, there is x > 0, when x > x, f (x) is bounded" wrong?
18. If both non-zero real numbers a and B have f (a + b) = f (a) * f (b) and if x 1, we prove that f (x) is a decreasing function
19. If the nonzero function f (x) has f (a + b) = f (a) &; f (b) for any real number A.B, and if x1, (1) prove that f (x) > 0 (2) prove that f (x) is a decreasing function (3) solve the inequality f (x-3) &; f (6-2x) ≤ 1 / 4 when f (4) = 1 / 16
20. If the non-zero function f (x) has f (a + b) = f (a) * f (b) for any real number a and B, and if X1 proves: F (x) > 0