Practice Flashcards
Flip to reveal answersWhat is the gradient of the tangent at x = a?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 9 Flashcards — Tangents
Sign up free to track progress and get spaced-repetition review schedules.
Question
What is the gradient of the tangent at x = a?
Answer
f'(a) — the derivative evaluated at a.
Question
What point does the tangent at x = a pass through?
Answer
(a, f(a)) — the point of contact on the curve.
Question
What form do you use for a tangent equation?
Answer
y − y₁ = m(x − x₁), with m = f'(a) and (x₁, y₁) = (a, f(a)).
Question
Where do you get the y-coordinate of the point of contact?
Answer
Substitute x = a into the original f(x), not into f'(x).
Question
What is the gradient of a horizontal tangent?
Answer
0.
Question
How do you find horizontal tangents?
Answer
Solve f'(x) = 0, then find the y-values.
Question
What form does a horizontal tangent take?
Answer
y = a constant (the y-coordinate of the point).
Question
What gradient does a tangent parallel to y = mx + c have?
Answer
The same gradient m as the line.
Question
Steps to find a tangent equation?
Answer
Differentiate → f'(a) for gradient; f(a) for the point; substitute into y − y₁ = m(x − x₁).
Read the notes
Full study notes for Tangents
Topic 5.4 hub
Tangents & normals
More from Topic 5.4
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