Question

Дана функция Найти f'(0)

Answer 1

F(x) = cosx - x² 
         1-x      3

f(x)' = (cosx)' - 1/3 (x²)' = (cosx)' (1-x) - cosx (1-x)'  - (1/3) * 2x =
         ( 1-x  )                                (1-x)²
     = -(1-x) sinx + cosx   -  2x  
                   (1-x)²              3 
f' (0)= -(1-0) sin 0 + cos 0  - 2*0 =  1/1 =1
                     (1-0)²                 3

Answer 2

Finding f'(0)

To find f'(0), we need to determine the derivative of the function f(x) at x = 0. Unfortunately, the given question does not provide the function f(x) explicitly. However, we can try to find the function f(x) based on the available information.

From the search results, we have some snippets that mention functions and their derivatives. Let's examine them to see if we can find any relevant information.

Snippet from Source ``` Feb 17, 2013 ... . f(x)=x^3/3-2x^2-12x+5. f ' (x)=0. ( ). 2. ... ```

This snippet mentions a function f(x) = x^3/3-2x^2-12x+5 and its derivative f'(x) = 0. However, it does not specify the value of x at which the derivative is zero.

Snippet from Source ``` Mar 19, 2010 ... f (x) = [x] - , ... = 0 . 5.2 lim x0. (1 + 2x). 3 x . ... ```

This snippet mentions a function f(x) = [x] - ..., but it does not provide any information about the derivative.

Unfortunately, none of the available snippets provide the exact function f(x) and its derivative at x = 0. Without this information, we cannot determine the value of f'(0).

If you have any additional information or if there is another way to approach the problem, please let me know, and I'll be happy to assist you further.