Question

Обчисліть f'(2),якщо f(x)=х^3

Answer 1

Ответ:

Пошаговое объяснение:

f(x)=x^3,  f'=3x^2,  f'(2)=3*2^2=3*4=12

Answer 2

To calculate the derivative of the function f(x) = x^3 and find its value at x = 2, we can use the power rule of differentiation.

The power rule states that if we have a function of the form f(x) = x^n, then its derivative f'(x) is given by f'(x) = n * x^(n-1).

In this case, n = 3, since f(x) = x^3. So, the derivative of f(x) is:

f'(x) = 3 * x^(3-1) = 3 * x^2

Now, we need to find f'(2). Plugging x = 2 into the derivative, we get:

f'(2) = 3 * 2^2 f'(2) = 3 * 4 f'(2) = 12

Therefore, the value of f'(2) for the function f(x) = x^3 is 12.