Introduction to derivatives
Practice Flashcards
What is the gradient of a curve at a point?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All Flashcards in Topic 5.1
Below are all 9 flashcards for this topic. Sign up free to track your progress and get personalized review schedules.
5.1.19 cards
What is the gradient of a curve at a point?
The gradient of the tangent to the curve at that point.
What does the derivative measure?
The gradient at a point and the instantaneous rate of change of y with respect to x.
Why doesn't a curve have a single gradient?
Its steepness changes from point to point, so the gradient depends on where you are.
What are the two notations for the derivative?
f'(x) and dy/dx.
How do you find the gradient at a particular x?
Substitute the x-value into the gradient function f'(x).
What does f'(x) > 0 tell you?
The function is increasing there.
What does f'(x) < 0 tell you?
The function is decreasing there.
What does f'(x) = 0 tell you?
There is a stationary point (the curve is momentarily flat).
If s is distance and t is time, what is ds/dt?
The velocity — the rate of change of distance with time.
Topic 5.1 study notes
Full notes & explanations for Introduction to derivatives
Math AA SL exam skills
Paper structures, command terms & tips
Want smart review reminders?
Sign up free to track your progress. Our spaced repetition algorithm will tell you exactly which cards to review and when.
Start Free