Differentiation Flashcards
1
Q
Describe what differentiation is
A
is the process of finding the gradient function
2
Q
derivative of x^n
A
nx^n-1
3
Q
derivative of kx^n
A
knx^n-1
4
Q
derivative of k
A
0 because k is a constant
5
Q
tangents and normals to curves
A
- gradient of tangent to a curve at a specific point is the same as the gradient of the curve at that point
- normal to a curve is the line perpendicular to the tangent - m’ = - 1/m
6
Q
Increasing function
A
when dy/dx > 0
7
Q
Decreasing function
A
when dy/dx < 0
8
Q
Stationary points
A
these points occur when the gradient is 0
9
Q
Types of stationary points
A
- local maximum
- local minimum
10
Q
Local maximum
A
gradient +ve -> gradient 0 -> gradient-ve
11
Q
Local minimum
A
gradient -ve -> gradient 0 -> gradient +ve
12
Q
Rules for sketching the graph of a derivative
A
- when there is a turning point, f’(x) is 0 so the graph crosses the x-axis
- when the graph is increasing, f’(x) is positive so the graph will be above the x-axis
- when the graph is decreasing, f’(x) is negative so the graph will be below the x-axis
