Let be continuous on and differentiable on

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

Problem

Let

f

be continuous on

[a,b]

and differentiable on

(a,b)

. Which one of the following conditions is sufficient to conclude that

f

is strictly increasing on

(a,b)

? (a)

f'(x)\ge 0\text{ for every } x\in(a,b)

(b)

f'(x)>0\text{ for at least one } x\in(a,b)

(c)

f'(x)=0\text{ for at least one } x\in(a,b)

(d)

f'(x)>0\text{ for every } x\in(a,b)