differentiation & integration Flashcards
1
Q
how do you determine if the graph is concave or convex (using the stationary points)
A
- if the stationary point is greater than zero (minimum point) then the curve is convex
- if the stationary point is less than zero (maximum point) the graph is concave
2
Q
how do you find the coordinates of any non-stationary points of inflection
A
- find the second derivative and make it equal to zero and then solve the equation to find x and then add the value into the equation to find the y-value
3
Q
what are stationary points
A
- points on a graph where the curve flattens out – when the gradient is 0
4
Q
what happens when a function is increasing vs decreasing
A
- when a function is increasing the gradient is positive and y gets bigger as x gets bigger
- when a function is decreasing the gradient is negative y gets smaller as x gets bigger
5
Q
what is a point of inflection
A
- when the graph changes between concave (curving upwards) and convex (curving downwards)
- they can also be stationary points
6
Q
chain rule formula
A
dy/dx = dy/du x du/dx
7
Q
product rule formula
A
- lefty righty, righty lefty
- u dv/dx x v du/dx
8
Q
quotient rule formula
A
v du/dx - u dv/dx all over v²
9
Q
e an lnx differentiated
A
- e^x differentiated will be e^x
- lnx differentiated will be 1/x
10
Q
tanx integrated
A
ln | sec x | + c
