Suppose a function is continuous on and differentiable on

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Suppose a function

f

is continuous on

[a,b]

and differentiable on

(a,b)

. It has exactly one critical number

c

(a,b)

, and

f''(c)>0

. Which of the following MUST be true? (a)

f

attains its absolute maximum at

x=c

on the interval

[a,b]

. (b)

f

attains its absolute minimum at

x=c

on the interval

[a,b]

. (c)

f

attains both its absolute minimum and its absolute maximum at

x=c

[a,b]

. (d)

f

attains its absolute minimum at one of the endpoints

x=a

x=b

of the interval

[a,b]