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Flip to reveal answersHow do you find the gradient of a curve at x = a?
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All 9 Flashcards — Gradient at a point
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Question
How do you find the gradient of a curve at x = a?
Answer
Differentiate to get f'(x), then substitute x = a to get f'(a).
Question
Which comes first: differentiate or substitute?
Answer
Differentiate first, then substitute the value.
Question
How do you find where a curve has gradient m?
Answer
Set f'(x) = m and solve for x.
Question
Why might 'find where the gradient is m' have two answers?
Answer
If f'(x) is a quadratic, f'(x) = m can have two solutions.
Question
How is a tangent's gradient related to its angle with the x-axis?
Answer
Gradient = tan(angle).
Question
Gradient of a tangent making 45° with the x-axis?
Answer
tan 45° = 1.
Question
Where does a curve have a horizontal tangent?
Answer
Where f'(x) = 0.
Question
Gradient at a point: substitute into f or f'?
Answer
Into f'(x) (the derivative), not f(x).
Question
Find x where y = x² has gradient 8?
Answer
2x = 8 ⇒ x = 4.
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Full study notes for Gradient at a point
Topic 5.3 hub
Differentiating polynomials
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Math AA SL exam skills
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