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Flip to reveal answersWhat is the normal to a curve at a point?
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All 9 Flashcards — Normals
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Question
What is the normal to a curve at a point?
Answer
The line through the point that is perpendicular to the tangent there.
Question
What is the gradient of the normal?
Answer
−1/f'(a) — the negative reciprocal of the tangent's gradient.
Question
How do you get the normal gradient from the tangent gradient?
Answer
Flip it and change the sign (negative reciprocal).
Question
What point does the normal pass through?
Answer
The same point of contact (a, f(a)) as the tangent.
Question
Tangent gradient 2 → normal gradient?
Answer
−1/2.
Question
Tangent gradient −3 → normal gradient?
Answer
+1/3.
Question
What is the normal at a stationary point?
Answer
A vertical line x = a (since the tangent is horizontal).
Question
Why can't you use −1/f'(a) at a stationary point?
Answer
f'(a) = 0, so −1/0 is undefined; geometrically the normal is vertical.
Question
Method to find a normal equation?
Answer
Find f'(a), take −1/f'(a), find the point (a, f(a)), then y − y₁ = m(x − x₁).
Read the notes
Full study notes for Normals
Topic 5.4 hub
Tangents & normals
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