Question

Find the local maximum and minimum values of f using both the First and Second Derivative Tests.
f(x) = x5 - 5x + 6

Answer 1

First derive the function once to find the critical numbers, then you can derive once more and substitute the critical numbers there to find the local min and max, but beware!

if the answer < 0, then it's a local max
if the answer > 0 then it's a local min ( not sure of this rule though)

but in a much simpler way:

1) derive once,
2) find the critical points by taking the 2 conditions when f'(x) = 0 and f'(x) = UND
3) substitute the critical numbers in the original function
4) The largest is the local max, the smallest is the local min

Give it a try now ^_^ good luck!