Step-by-step explanation:
Given: f(x) = 3x^2 − 6x + 1. x ∈ (-∞, ∞)
now differentiating f(x) w.r.t. x we get
f'(x) = 6x-6
equating it 0 we get
x = 1, which is a critical point
Now using second derivative test to check relative maxima or minima
f''(x) = 6 >0
⇒ x=1 is a relative minima.
also, x=1 f(1) = 3-6+1 = -2
