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Flip to reveal answersWhat is the gradient of a curve at a point?
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All 9 Flashcards — Derivative as gradient
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Question
What is the gradient of a curve at a point?
Answer
The gradient of the tangent to the curve at that point.
Question
What does the derivative measure?
Answer
The gradient at a point and the instantaneous rate of change of y with respect to x.
Question
Why doesn't a curve have a single gradient?
Answer
Its steepness changes from point to point, so the gradient depends on where you are.
Question
What are the two notations for the derivative?
Answer
f'(x) and dy/dx.
Question
How do you find the gradient at a particular x?
Answer
Substitute the x-value into the gradient function f'(x).
Question
What does f'(x) > 0 tell you?
Answer
The function is increasing there.
Question
What does f'(x) < 0 tell you?
Answer
The function is decreasing there.
Question
What does f'(x) = 0 tell you?
Answer
There is a stationary point (the curve is momentarily flat).
Question
If s is distance and t is time, what is ds/dt?
Answer
The velocity — the rate of change of distance with time.
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Full study notes for Derivative as gradient
Topic 5.1 hub
Introduction to derivatives
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Math AA SL exam skills
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