Polynomials Flashcards
What’s an increasing function?
It’s the part of a function when the y/result is getting bigger.
What’s a decreasing function?
It’s the part of a function when the y/result is getting smaller.
What’s a turning point?
It’s when the gradient is zero and immediately to one side it is an increasing function and immediately to the other it is a decreasing function.
What’s a maximum point?
Gradient is zero, increasing to the left, decreasing to the right
What’s a minimum point?
Gradient is zero, increasing to the right, decreasing to the left
What is a point of inflection?
It’s when the gradient is zero but it’s not a turning point because it’s still an increasing/decreasing function.
How many turning points can an order of 3 have?
Either 2 or 0
How many turning points can an order of 4 have?
Between 3 and 1
What’s the max num of turning points that an order of n can have?
n-1
Which amounts of turning points or points of inflection can an order of n have?
the possible amounts of roots for n-1. (technically wasn’t taught this but figured it out and it could come in handy). I AM PRETTY SURE THIS DOES NOT INCLUDE REPEATED ROOTS IN PREVIOUS ONES, AKA THSE COUNT AS 2 TURNING POINTS NOT ONE.
Factor Theorem
For f(x), if f(a) = 0 then (x-a) is a factor of f(x).
Eg.
f(x)= x^2 -2x +1
f(1)= 0
therefor (x^2 -2x +1)/(x-1) will give a whole number.
How could you use factor theory to solve a function of >2 orders of magnitude?
If you can, figure out roughly what range one of the answers has to be in. Use the table function (hopefully only changing the number it’s trying by 1 each time). If any of them are zero then use long division to divide the function by (x-n). Either repeat or solve or whatever the situation requires.
