🟢 5.2.5 Assignment 5 of 5

• 1

• 0

• f does not have an abs min value.

Mathematical Equivalence

ON

The function f is defined for all x in the closed interval [a, b]. If f does not attain a maximum value on [a,b], which of the following must be true?

• f is not continuous on .[a,b]

• f is not bounded on .[a,b]

• f does not attain a min value on [a,b].

• The graph of f has a vertical asymptote in the interval [a,b]

• f'(x)=0 does not have a solution on the interval [a,b]

• f'(c)=0 for some c such that a<c<b.

Mathematical Equivalence

ON

If f is a continuous function on the closed interval [a, b], which of the following must be true?

• There is a number c in the open interval (a, b) such that f (c) = 0.

• There is a number c in the open interval (a, b) such that f (a) < f (c) < f (b).

• There is a number c in the closed interval [a, b] such that f (c) ≥ f (x) for all x in [a, b].

• There is a number c in the open interval (a, b) such that f'(c)=0