Exam 2; chapter 3-5 Flashcards
relative maximum
Y Value that corresponds to the highest x value in function.
ex:
(max is # located at x= #)
increasing from left
decreasing from right
relative minimum
Y Value that corresponds to the lowest x value in function.
ex:
( min is # located at x=# )
decreasing from left
increasing from right
NO relative extrema
when there is no change in signs!
it is increasing on both sides
OR
it is decreasing on both sides
critical number
x values
Only places where the sign can change
to find set f’(x)= 0
to test point on a line
test random points before/ after the critical points
to find points (x,y)
plug x values into original equation
The y value
determines whether a point on a function is a relative extremum
The x value
is the location of the extremum
limits
Y values that are aprroaching a certain x value.
+ : aproaching from right
- : aproaching from left
if there are two points, pick the point represented by the closed circle.
closed circle : ≤ or ≥
open circle : < or >
limits
The x-values determine where we are “approaching” on the input axis (the horizontal axis).
The y-values are what the limit describes—the behavior or value that 𝑓(𝑥) (the output of the function) is approaching as x gets closer to a particular number.
continuous
both f(x) and lim f(x) have to exist! and be the same.
has to be smooth curves and connected to the function
NO sharp corners : v or / or |
slope of secant line
f(b)-f(a) / b-a
slope of tangent line
f(x+h)- f(x) / h
f increases
if the slope of tangent line is possitive
rate of change of distance
speed
rate of change of speed
acceleration
