Mathematics

Problem

For a function

f

defined on the interval

[a,b]

, which of the following sets of hypotheses is SUFFICIENT to guarantee that a point

x=c

with

f'(c)=0

and

f''(c)>0

is the absolute minimum of

f

[a,b]

? a)

f''(x)>0

for all

x

(a,b)

but

f

need not be continuous at the endpoints. b)

f

is continuous on

[a,b]

and

c

is the only critical point of

f

(a,b)

. c)

f

is continuous on

(a,b)

only. d)

f

is continuous on

[a,b]

but may have other critical points in

(a,b)