unit 4 Flashcards
x = — is a critical point of f because
f’ = 0 or is undefined
x = — is a relative MAXimum of f because
f’ changes from positive to negative
+ –> -
POS to NEG
x = — is a relative MIN of f because
f’ changes from negative to positive
- –> +
NEG to POS
x = — is neither a max nor min because
f’ does not changes signs
f is increasing on ( , ) because
f’ > 0
above x-axis
f is decreasing on ( , ) because
f’ < 0
below x-axis
x = — is a point of inflection because
f’’ (the slope of f’) = 0 or is undefined AND changes signs
f is concave UP on ( , ) because
f’’ (the slope of f’) > 0
+
f is concave DOWN on ( , ) because
f’’ (the slope of f’) < 0
-
if f(x) = integral from x to number of g(t) dt, then
g’(x) = f(x)
steps to find relative extrema
- find derivative
- set equal to 0
- solve for critical points
- make table of values, include interval values, and critical points
> plug in x-values into og function
rel min at — when x = — (smallest y-value)
rel max at — when x — (largest y-value)
how to know if rolle’s theorem applies ?
set f(a) and f(b) equal to each other, if it’s true then rolle’s does apply
f(a) = f(b) then rolle’s applies
how to determine values of c guaranteed by the MVT ?
find derivative of function
set equal to 0, and find c
make sure it’s in the interval !!!
what must be met for mvt to apply ?
function must be continuous and differentiable
how to find critical points ?
find derivative
set equal to 0 and find x
critical points are x
