Differentiation Flashcards
1
Q
how to show a value is minimum (no 2nd derivative)
A
gradients of values either side of the point
2
Q
how to show a value is maximum (no 2nd derivative)
A
gradients of values either side of the point
3
Q
how to show a value is minimum (2nd derivative)
A
2nd derivative > 0
4
Q
how to show a value is maximum (2nd derivative)
A
2nd derivative < 0
5
Q
first principle: limit formula
A
lim(f(x+h) - f(x)/h)
6
Q
first derivative, decreasing
A
f’(x) < 0 - decreasing
7
Q
first derivative, stationary
A
f’(x) = 0 - stationary
8
Q
first derivative, increasing
A
f’(x) > 0 - increasing
9
Q
second derivatives, max point
A
f’‘(x) < 0 - max point
10
Q
second derivatives, point of inflection
A
f’‘(x) = 0 - point of inflection
11
Q
second derivatives, min point
A
f’‘(x) > 0 - min
