Question

what is the second derivative test? and how do you use it?

Answer 1

the second derivative test tests the intervals in which the first derivative is increasing/decreasing. if the first derivative is increasing, the function is concave up. if the first derivative is decreasing, the funciton is concave down....

Answer 2

isnt it the opposite?

Answer 3

if first derivative is increasing then its concave down?

Answer 4

no... first derivative increasing means the slope of the tangent line is increasing.. so concave up.

the second derivative test is like the first derivative test in that it tests for local max/min. by plugging in the critical numbers in the second derivative.

Answer 5

okay how would you use the second derivative test to find the local extrema.
f(x)=(3-2x)^4

Answer 6

take first then second derivative... first..

Answer 7

first derivative = 8(3-2x)^3

Answer 8

and would the critical # be 3/2?

Answer 9

sorry internet is not working properly...

Answer 10

ok

Answer 11

cr# is correct. now plug that into your second derivative

Answer 12

notice you get f'' = 0 there. the second derivative test fails.

Answer 13

yes, so now what would i do?

Answer 14

for instance, for f" i got >0, what would that mean?

Answer 15

that would mean your critical number is at a place in your function where it is concave up... therefore you have a local min.

Answer 16

so if the second derivative test fails, what would you do?