Find whether x=3 is a local maximum or a local minimum and Sketch the graph.
The function f has a derivative everywhere and has just one critical point, at x=3. In parts (a) to (d), you are given additional conditions. In each case decide whether x=3 is a local maximum, a local minimum, or neither. Explain your reasoning. Sketch possible graphs for all four cases.
(a)f '(1) = 3 and f '(5) = -1
(b)f (x) → ∞ as x → ∞ and as x → - ∞
(c)f (1) = 1, f (2), f (4) = 4, f (5) =5
(d)f '(2) = -1, f (3) =1, f (x) → 3 as x→ ∞