Question

Найдите f'(2), если f(x)=2x²-3x+1

Answer 1

Ответ: будет    f(x)=(2x-1)умножить(x-1)

Answer 2

To find the derivative of the function f(x) with respect to x and then evaluate it at x = 2, we can use the power rule for differentiation. The power rule states that the derivative of x^n is nx^(n-1), where n is a constant.

Given the function f(x) = 2x² - 3x + 1, let's find its derivative f'(x):

f'(x) = d/dx [2x²] - d/dx [3x] + d/dx [1]

Now, apply the power rule:

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

f'(x) = 4x - 3

Now, to find f'(2), substitute x = 2 into the derivative:

f'(2) = 4 * 2 - 3

f'(2) = 8 - 3

f'(2) = 5

So, the value of f'(2) is 5.