Question
Find the local maximum and minimum values of f, using both the First and the Second Derivative Tests
f(x) = x^2/x - 1
f(x) = x^2/x - 1
Answers
oobleck
I assume you mean
f(x) = x^2/(x-1)
f'(x) = x(x-2)/(x-1)^2
so f'=0 at x=0,2 and the local extrema are at (0,0) and(2,4)
f"(x) = 2/(x-1)^3
f"(0) = -2 < 0 so (0,0) is a max
f"(2) = 2 > 0 so (2,4) is a min
now be sure to read the question carefully
f(x) = x^2/(x-1)
f'(x) = x(x-2)/(x-1)^2
so f'=0 at x=0,2 and the local extrema are at (0,0) and(2,4)
f"(x) = 2/(x-1)^3
f"(0) = -2 < 0 so (0,0) is a max
f"(2) = 2 > 0 so (2,4) is a min
now be sure to read the question carefully