Practice Flashcards
Flip to reveal answersWhat is the second derivative?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 9 Flashcards — Second derivative
Sign up free to track progress and get spaced-repetition review schedules.
Question
What is the second derivative?
Answer
The derivative of the first derivative — differentiate f(x) twice.
Question
How is the second derivative written?
Answer
f''(x) or d²y/dx².
Question
What does f''(x) > 0 mean for the curve?
Answer
It is concave up (∪).
Question
What does f''(x) < 0 mean for the curve?
Answer
It is concave down (∩).
Question
State the second-derivative test.
Answer
At a stationary point: f'' > 0 → minimum, f'' < 0 → maximum.
Question
What if f''(x) = 0 at a stationary point?
Answer
The test is inconclusive; check the sign of f' on each side instead.
Question
How do you find where a curve is concave up?
Answer
Solve f''(x) > 0.
Question
If f(x) = x³ − 4x², what is f''(x)?
Answer
f'(x) = 3x² − 8x, so f''(x) = 6x − 8.
Question
What does the second derivative measure?
Answer
How the gradient (first derivative) is changing — the curve's bending.
Read the notes
Full study notes for Second derivative
Topic 5.7 hub
Second derivative
More from Topic 5.7
All flashcards in this topic
Math AA SL exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free