-take 2nd derivative
-set equal to 0
-set up number line
-plug points into 2ND DERIVATIVE

Back

rolle's theorem

Front

1) check that you can use rolle's theorem
-is it continuous?
-is it differential?
-are the outputs the same?
2) set derivative = to 0

Back

mean value theorem

Front

f(x) has to be continuous and differentiable
defined over [a, b] (for closed--all numbers from a-b including a and b--versus open (a, b) which means all numbers from a-b not including a and b)
if this is true, f'(c)=f(b)-f(a)/(b-a)

Back

extrema

Front

extrema = relative min or max
derivative of the function = 0
plug in points to find where increasing a decreasing
decreasing to the left and increasing to the right = local min
increasing to the left and decreasing to the right = local max

Back

critical values

Front

-relative min/max only occur at cv
cv are f'(c) = 0 or f'(c) = undef