Question

Найти при каких значениях x производная функции f(x)=3x^2-12x+5 равна нулю?

Answer 1

1. Дифференцируем нашу функцию

$f'(x)=(3x^2-12x+5)'=6x-12$

2. Приравниваем продифференцированную функцию к нулю

$6x-12=0 \\ 6x=12 \\ x=2$

Ответ: $x=2$

Answer 2

f'(x) =3*2x-12=6x-12

f'(x)=0

6x-12=0

6x=12

x=12:6

x=2

Answer 3

To find the values of x where the derivative of the function f(x) = 3x^2 - 12x + 5 is equal to zero, we need to find the critical points of the function. Critical points occur where the derivative is either zero or undefined.

Let's first find the derivative of f(x) with respect to x:

f'(x) = d/dx (3x^2 - 12x + 5)

To find the derivative, we apply the power rule:

f'(x) = 2 * 3x^(2-1) - 1 * 12x^(1-1) + 0 f'(x) = 6x - 12

Now, we set the derivative equal to zero and solve for x:

6x - 12 = 0

Adding 12 to both sides:

6x = 12

Dividing both sides by 6:

x = 2

So, the value of x where the derivative of f(x) is equal to zero is x = 2.