APFIVE First Derivative Test for Local Extrema
A researcher analyzes the function
$$f(x)=x^3-3*x^2+2$$
and computes its derivative as
$$f'(x)=3*x^2-6*x$$, yielding critical points at x = 0 and x = 2. They then mistakenly conclude that there is a local maximum at x = 2. Identify the error in their analysis.
A
There is no mistake; x = 2 is correctly identified as a local maximum.
B
The mistake lies in the differentiation process; the derivative of f(x) should have an additional constant term.
C
The error is due to an incorrect factorization of the function f(x).
D
The error is in the interpretation of the first derivative test; a proper sign analysis shows that x = 0 is the local maximum and x = 2 is a local minimum.
Question Leaderboard
Not enough data yet to show leaderboard.