Tangents & normals
Practice Flashcards
What is the gradient of the tangent at x = a?
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All Flashcards in Topic 5.4
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5.4.19 cards
What is the gradient of the tangent at x = a?
f'(a) — the derivative evaluated at a.
What point does the tangent at x = a pass through?
(a, f(a)) — the point of contact on the curve.
What form do you use for a tangent equation?
y − y₁ = m(x − x₁), with m = f'(a) and (x₁, y₁) = (a, f(a)).
Where do you get the y-coordinate of the point of contact?
Substitute x = a into the original f(x), not into f'(x).
What is the gradient of a horizontal tangent?
0.
How do you find horizontal tangents?
Solve f'(x) = 0, then find the y-values.
What form does a horizontal tangent take?
y = a constant (the y-coordinate of the point).
What gradient does a tangent parallel to y = mx + c have?
The same gradient m as the line.
Steps to find a tangent equation?
Differentiate → f'(a) for gradient; f(a) for the point; substitute into y − y₁ = m(x − x₁).
5.4.29 cards
What is the normal to a curve at a point?
The line through the point that is perpendicular to the tangent there.
What is the gradient of the normal?
−1/f'(a) — the negative reciprocal of the tangent's gradient.
How do you get the normal gradient from the tangent gradient?
Flip it and change the sign (negative reciprocal).
What point does the normal pass through?
The same point of contact (a, f(a)) as the tangent.
Tangent gradient 2 → normal gradient?
−1/2.
Tangent gradient −3 → normal gradient?
+1/3.
What is the normal at a stationary point?
A vertical line x = a (since the tangent is horizontal).
Why can't you use −1/f'(a) at a stationary point?
f'(a) = 0, so −1/0 is undefined; geometrically the normal is vertical.
Method to find a normal equation?
Find f'(a), take −1/f'(a), find the point (a, f(a)), then y − y₁ = m(x − x₁).
Topic 5.4 study notes
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Math AA SL exam skills
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