Question

Consider the function f(x)=(x−4)3−2
. In which interval is the graph increasing?(1 point)
Responses

(0,∞)
left parenthesis 0 comma infinity right parenthesis

(−∞,4)
left parenthesis negative infinity comma 4 right parenthesis

(−∞,∞)
left parenthesis negative infinity comma infinity right parenthesis

(4,∞)
left parenthesis 4 comma infinity right parenthesis

Answer 1

(−∞, ∞)

Reason: f'(x) = 3(x−4)^2 ≥ 0 for all x (and the cubic (x−4)^3 is strictly increasing), so the graph is increasing on the entire real line.