Let f (x) be differentiable in a neighborhood of x = 0, and lim f '(x) = 1, then f (x) has extremum in x = 0, and the detailed solution is obtained

How can f (x) have extremum when Lim f '(x) = 1?
When the derivative value is 0 or the derivative value does not exist,
It can be extreme
Is there something wrong with your title?

RELATED INFORMATIONS

1. X tends to 0) Lim [(x + 4) ^ 1 / 2-2] / sin3x
2. Lim x tends to 0 arcsin2x / sin3x
3. Let f (x) be differentiable at x0, then it is equal to Why Lim f (x + H) - f (X-H) / h = 2F '(x) Why 2F '(x), not 1 / 2 F' (x) F '(x) isn't that 2 in the denominator, and it becomes 1 / 2 after it is put forward?
4. Given that f (x) is differentiable at x0, then when h approaches 0, f (x0 + H) − f (x0 − h) 2H approaches () A. 12f′(x0)B. f′（x0）C. 2f′（x0）D. 4f′（x0）
5. It is known that the derivative of F (x) at x = x0 is 4, Lim [x → x0] [f (x) - f (x0)] / 2 (x0-x)]=_______
6. When h approaches 0, Lim H / F (A-H) - f (a) = 1 / 3, then the derivative of F (a) is
7. Let the function y = f (x) be defined in a certain interval, where x0 and x0 + Δ X are defined. What do x0 and x0 + Δ x mean
8. Given the function f (x) = x * 3-x * 2 + X / 2 + 1 / 4, it is proved that there exists x0 belonging to 0 to 1 / 2, such that f (x0) = x0
9. A necessary and sufficient condition for a function f (x) to be differentiable at point x0 is that the left and right derivatives of F (x) at point x0 exist and are equal. / / / / / / / / / / / / / / however, a necessary condition for differentiability is continuity. Is this contrary to the first proposition
10. For example, the derivative of continuous function is not necessarily continuous F (x) is differentiable everywhere on (a, b), but there exists x0 ∈ (a, b), so that f '(x0) exists, but f' (x) is discontinuous at x0 Who can give such an example?
11. Let f (x) be differentiable and find Lim [f (x + △ x)] ^ 2 - [f (x)] ^ 2 △ x → 0 lim [f(x+△x)]^2-[f(x)]^2 △x→0 =lim{[f(x+△x)+f(x)]*[f(x+△x)-f(x)]}/△x Why is it equal to ＝2f(x)lim[f(x+△x)-f(x)]/△x Especially why is it equal to 2F (x) Please give specific reasons,
12. Let f (x) be differentiable at point X. = 0, and f (0) = 0 and f '(0) = 3, then the value of LIM (x →∞) [f (x) / x] ()
13. Given that f (x) is differentiable at x = 0, f (0) = 0, f '(0) = 2, what is the limit of F (sin3x) / X when x approaches 0
14. Let f (x) be differentiable on [0,1], and f (1) = 2 ∫ 0 ~ 1 / 2 XF (x) DX. It is proved that there exists ξ belonging to (0,1), such that f (ξ) + ξ f '(ξ) = 1
15. It is proved that LIM (1-e ^ 1 / x) / (1 + e ^ 1 / x) does not exist when x tends to 0 LIM (1 / X of 1-e) / (1 / X of 1 + e) does not exist when x tends to zero
16. Why can derivative be written as f '(a) = LIM (x → a) f (x) - f (a) / x-a Shouldn't it be written as f '(x) = LIM (△ x → 0) (x + Δ x) - f (x) / Δ x? I hope you can help me
17. Let f (x) be differentiable at x = A and lim [f (a + 5H)] - f (a-5h)] / 2H = 1, then f '(a)=
18. Let f (x) be differentiable at x = 1 and f '(1) = 2, then [LIM (H → 0) f (1-h) - f (1)] / h is equal to
19. If the function f (x) is differentiable at x = a, then Lim h → 0 (f (a + 3H) - f (A-H)) △ 2H =?
20. Let f (x) be differentiable at x = 2 and f '(2) = 2, then Lim h → 0 [f (2-3H) - f (2)] / h =?