To prove that a differentiable function is strictly decreasing on an interval

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

Problem

To prove that a differentiable function

s

is strictly decreasing on an interval

(m,n)

, which additional hypothesis is sufficient? (a)

s'(x)\le 0

for all

x

(m,n)

and

s'(x)\neq 0

somewhere in

(m,n)

. (b)

s'(x)\ge 0

for all

x

(m,n)

. (c)

s'(x)<0

for all

x

(m,n)

. (d)

s'(x)

changes sign exactly once on

(m,n)