Math Problem Solver

Sketch a graph of a continuous function 𝑦 = 𝑓(𝑥), which is increasing on the interval

(−∞, ∞), and has an inflection point at 𝑥 = 1 and is concave up on (0, ∞).

For problems 4 – 8, calculate each of the following

(a) The intervals on which 𝑓(𝑥) is increasing

(b) The intervals on which 𝑓(𝑥) is decreasing

(c) The intervals on which 𝑓(𝑥) is concave up

(d) The intervals on which 𝑓(𝑥) is concave down

(e) All points of inflection. Express each as an ordered pair (x,y)

𝑓(𝑥) = 𝑥^3 − 2𝑥 + 3