05 Differentiation Flashcards
How do you differentiate?
Multiply by the power, then reduce the power by one.
What is dy/dx?
Differentiated equation
How do you find the gradient using differentiation?
Substitute the x coordinate into the in the dy/dx equation
What is the normal line?
A perpendicular line.
If dy/dx > 0 is the gradient increasing or decreasing?
Increasing.
If dy/dx < 0 is the gradient increasing or decreasing?
Decreasing.
What is the function version of dy/dx?
f ’(x)
What is the second derivative?
Differentiate twice
What is the symbol for the second derivative?
What is the function version of the 2nd derivative?
f ‘’(x)
At a stationary point what is dy/dx equal to?
0
How do you find the nature of a stationary point?
Use the second derivative.
If it is bigger than zero then it’s a min point.
If it’s smaller than zero then it’s a max point.
If its equal to zero then it’s a point of inflection.
When finding the nature of a stationary point, if you get the second derivative equal to zero what should you do?
It could be the point of inflection but not always. You should find dy/dx of each side of the stationary point and see that they are both increasing or decreasing.
If the second derivative is bigger than zero what is the nature of the stationary point?
Minimum point.
If the second derivative is smaller than zero then what is the nature of the stationary point?
Maximum point.
