11/14

so we learned about the second derivative test...

take the first derivative and set = 0
then take the second derivative set = 0 and solve for x.
check for differentiability; if it isnt differentiable, the test failed.

set up intervals with the x values from the second derivative
plug values from intervals into the second derivative
if the value is positive, the graph is concave up; if the value is negative, it is concave down

there is a shortcut:

take the first derivative and set = 0
check differentiability
plug in critical numbers into the second derivative
if it is positive, its a min. if it is negative, its a max. if it is zero, it fails.