Chapter 13 Flashcards
(14 cards)
How do you find the gradient of a curve at a specific point?
Draw a tangent to the curve at that point.
Define derivative/gradient function.
A function that gives the gradient of a graph at any point.
What happens to the gradient when the graph is increasing?
Positive.
What happens to the gradient when the graph is decreasing?
Negative.
Define stationary point.
A point on the graph where the tangent is horizontal and the gradient is zero.
Define a chord.
A line segment between two points on a curve.
What is the equation for differentiation from first principles?
f’(x) = lim(h - 0) f(x+h) - f(x)/h
Define differentiation.
The process of finding the derivative.
What is the value of dy/dx when y = x^n?
nx^n-1.
What is y’ when y = kf(x)?
kf’(x).
What is y’ for y = f(x) + g(x?)
y’ = f’(x) + g’(x).
What does the derivative show?
gradient/ rate of change of y with respect to x.
What does it mean if dy/dx is positive/negative?
Function is increasing/decreasing.
What does the second derivative show?
Rate of change of the gradient.
