For the function
f(x)=x3−12x+5f(x) = x^3 - 12x + 5f(x)=x3−12x+5
find the critical points and then use the sign of f′f'f′ on either side of each one to classify it.
Which statement is correct?
Select all that apply.
fff has a local maximum at x=−2x = -2x=−2 and a local minimum at x=2x = 2x=2.
fff has a local minimum at x=−2x = -2x=−2 and a local maximum at x=2x = 2x=2.
fff has a local maximum at x=−23x = -2\sqrt{3}x=−23 and a local minimum at x=23x = 2\sqrt{3}x=23.
x=−2x = -2x=−2 and x=2x = 2x=2 are critical points, but neither is an extremum — the curve just flattens there, the way x3x^3x3 does at 000.