Which set of hypotheses on a real-valued function defined on is sufficient to…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Which set of hypotheses on a real-valued function

f

defined on

[a,b]

is sufficient to guarantee that some number

c

(a,b)

satisfies

f'(c)=0

? (a)

f

is continuous on

(a,b)

, differentiable on

(a,b)

, and

f(a)=f(b)

. (b)

f

is continuous on

[a,b]

, differentiable on

(a,b)

, and

f(a)=f(b)

. (c)

f

is continuous on

[a,b]

, differentiable on

(a,b)

, with no restriction on

f(a)

and

f(b)

. (d)

f

is continuous on

[a,b]

, differentiable on

(a,b)

, and

f(a)<f(b)