Differentiation Flashcards
What is the concave region of a graph
the rate of change of the gradient is decreasing
What is the point of inflection region of a graph
The point of the graph where the gradient isn’t increasing or decreasing
what is the convex region of the graph
where the rate of change of the gradient is increasing
how to find the stationary points on a graph
1) differentiate the equation
2) set to 0 then solve for X
how to tell whether a stationary point is a minimum or a maximum
1) find the stationary points
2) differentiate again
3) set on of them = 0
if it is > 0 then it is a minimum
if it is , 0 it is a maximum
4) then do it for the other X value
What is the difference between maximmum/minimum points and concave/convex points?
concave and convex points aren’t looking at a single point but a set of points
How to find the concave/convex points on a graph
basically the same as a minimum/maximum point, but after differentiating a second time
Put a stationary point in and if it is <= 0 it is concave
and if it is >= 0 it is convex
what is the difference between a stationary point of inflection and a non stationary point of inflection
How to implicit differentiate
steps:
1) differentiate all terms, any terms with y put (dy/dx) next to them
-> If there are X and y terms together use the product rule to differentiate
2) collect all the terms with (dy/dx) next to them on one side and the rest on the other
3) factor out dy/dx
4) then divide by the terms that are inside the brackets of dy/dx
If a line is to the normal of another how do you find the gradient(m) of the normal line
the negative reciprocal of the other gradient
How to proof a^x
How to do chain rule differentiation
Steps:
1) bring the derivative inside the brackets to the front
2) bring the power down and minus 1 off of it
3) multiply it by the derivative and the brackets
Product rule formula
Quotient rule formula
need to do differentiation of first principals
proof of it
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