Mark each statement True or False. Justify each answer. (a) Let f : [a, b ] → be continuous and suppose f (a) (b) Let f : [a, b ] → be continuous and suppose f (a) ≤ k ≤ f (b). Then there exists a...

Mark each statement True or False. Justify each answer.

(a) Let f : [a, b ] →

be continuous and suppose f (a) <><>

(b) Let f : [a, b ] →

be continuous and suppose f (a) ≤ k ≤ f (b). Then there exists a point c ∈ [a, b ] such that f (c) = k.

(c) If f : D →

is continuous and bounded on D, then f assumes maximum and minimum values on D