Question

Дана функция f(x)= x^3/3-x^2-3x+10 решите уравнение f'(x)=0

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the equation f'(x) = 0, we first need to find the derivative of the function f(x) and then set it equal to zero.

Given the function f(x) = x^3/3 - x^2 - 3x + 10, let's find its derivative f'(x):

f'(x) = d/dx (x^3/3 - x^2 - 3x + 10) = d/dx (x^3/3) - d/dx (x^2) - d/dx (3x) + d/dx (10) = (1/3) * d/dx (x^3) - d/dx (x^2) - 3 * d/dx (x) + 0 = (1/3) * 3x^2 - 2x - 3 = x^2 - 2x - 3

Now, set f'(x) equal to zero and solve for x:

x^2 - 2x - 3 = 0

To factor this quadratic equation, we look for two numbers whose product is -3 and whose sum is -2.

The numbers are -3 and 1: (x - 3)(x + 1) = 0

Now, set each factor to zero and solve for x:

1. x - 3 = 0 x = 3

2. x + 1 = 0 x = -1

So, the solutions to the equation f'(x) = 0 are x = 3 and x = -1.