To find the derivative of the function f(x) = 3x² - 6x + 2, we can use the power rule for differentiation.
The power rule states that if we have a term of the form ax^n, the derivative with respect to x is given by nx^(n-1).
Applying the power rule to each term of f(x), we get:
f'(x) = d/dx(3x²) - d/dx(6x) + d/dx(2)
Taking the derivative of each term:
f'(x) = 2(3)x^(2-1) - 6(1)x^(1-1) + 0
Simplifying:
f'(x) = 6x - 6
Now, to find f'(1), we substitute x = 1 into the derivative:
f'(1) = 6(1) - 6 = 6 - 6 = 0
Therefore, f'(1) = 0.