Apply the second derivative test to
f(x)=x3−3x2−9x+7f(x) = x^3 - 3x^2 - 9x + 7f(x)=x3−3x2−9x+7
Find every critical point, classify each one, and compute the value of fff there.
Which statement is correct?
Select all that apply.
Local minimum value 121212 at x=−1x = -1x=−1, and local maximum value −20-20−20 at x=3x = 3x=3.
Local maximum value 121212 at x=−1x = -1x=−1, and local minimum value −20-20−20 at x=3x = 3x=3.
The only turning point is x=1x = 1x=1, where f′′=0f'' = 0f′′=0; the value there is −4-4−4.
The critical points are x=1x = 1x=1 and x=−3x = -3x=−3: a local maximum of value −20-20−20 at x=−3x = -3x=−3, and the test is inconclusive at x=1x = 1x=1.