Assume f is differentiable and has just one critical point, at x = 3. In parts (a) - (d), you are given additional conditions. In each case decide whether x = 3 is a local maximum, a local minimum, or neither. You should be able to sketch possible graphs for all four cases.

Assume / is differentiable and has just one critical point, at x = 3. In parts (a) - (d), you are given additional conditions. In each case (a) / '(0) = 4 and / '(9) = -1 O x = 3 is a local maximum. x = 3 is a local minimum O x = 3 is neither a local maximum nor a local minimum. (b) lim ((x) = * and lim (x) = O x = 3 is a local maximum. O x = 3 is a local minimum O x = 3 is neither a local maximum nor a local minimum. (c) (1) = 4, 1(2) - 5, /(4) = 6, and /(5) = 7 O x = 3 is a local maximum. O x = 3 is a local minimum O x = 3 is neither a local maximum nor a local minimum. (d) f '(2) = -1, /(3) = 1, and lim /(x) = 3 O x = 3 is a local maximum. O x = 3 is a local minimum O x = 3 is neither a local maximum nor a local minimum