What can you conclude about f if f is continuous on [0, 4], differentiable on (0, 4), and f '(x) 0 on (0, 4)? Mark all that apply. I.f is increasing on (0, 4)
II.f is increasing on [0, 4]
III.f is nondecreasing on (0, 4)
IV.f is nondecreasing on [0, 4]
A)I
B)I, II
C)I, II, III
D)I, II, III, IV

Question

What can you conclude about f if f is continuous on [0, 4], differentiable on (0, 4), and f '(x)> 0 on (0, 4)? Mark all that apply. I.f is increasing on (0, 4)
II.f is increasing on [0, 4]
III.f is nondecreasing on (0, 4)
IV.f is nondecreasing on [0, 4]
A)I
B)I, II
C)I, II, III
D)I, II, III, IV

Quizplus · Accepted Answer

Given that $f'(x) > 0$ on $(0, 4)$, it means $f$ is increasing on $(0, 4)$. Since $f$ is continuous on $[0, 4]$, it implies $f$ is also increasing on $[0, 4]$. Increasing functions are also nondecreasing, so all statements are true.

What Can You Conclude About F If F Is Continuous