Introduction to Differentiation
Practice Flashcards
Flip to reveal answersWhat does the derivative f′(x) tell you?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Introduction to Differentiation
Sign up free to track progress and get spaced-repetition review schedules.
Question
What does the derivative f′(x) tell you?
Answer
f′(x) is the gradient function. It gives the gradient of the curve y = f(x) at any x-value. Substitute a number into f′(x) to get the gradient at that point.
💡 Hint
Think: steepness, not height.
Question
What does the notation dy/dx mean?
Answer
dy/dx is "the derivative of y with respect to x". It is exactly the same thing as f′(x). Both notations appear in IB papers.
Question
What is the sign of f′(x) when the curve is rising?
Answer
f′(x) > 0 when the curve is increasing (rising left to right). f′(x) < 0 when decreasing. f′(x) = 0 at a local maximum or minimum.
Question
A curve has a local maximum at x = 3. What is f′(3)?
Answer
f′(3) = 0. At any local maximum (or minimum), the tangent is horizontal, so the gradient is zero.
💡 Hint
Flat tangent = zero gradient.
Question
Why does a straight line NOT need differentiation to find its gradient?
Answer
A straight line has the same gradient everywhere. For y = mx + c, the gradient is always m. Only curves have a different gradient at each point.
Question
V(t) is the volume (litres) in a tank. What does V′(t) = −5 mean?
Answer
The volume is decreasing at a rate of 5 litres per unit time. The negative sign means the function is falling. Always include units in your interpretation.
💡 Hint
Rate of change — always state units.
Question
What is the difference between f(a) and f′(a)?
Answer
f(a) is the y-value (height) of the curve at x = a.\nf′(a) is the gradient (steepness) of the curve at x = a.\nThey are completely different quantities.
Question
A curve is high up on the graph (large y-value) at x = 5, but f′(5) = 0. Is that possible?
Answer
Yes. f(x) and f′(x) are independent. A curve can be at any height while being momentarily flat — for example, at the top of a hill.
Read the notes
Full study notes for Introduction to Differentiation
Topic 5.3 hub
Introduction to derivatives
More from Topic 5.3
All flashcards in this topic
Math AI 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