MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider the function
f(x)=x4−4x3+6x2+1, for all x∈R.
Answer the following:
(i) Obtain f′(x).
(ii) Find all critical points of f.
(iii) Using appropriate reasoning based on f′(x), decide the nature of each critical point and hence determine every local maximum and local minimum value of f.
(iv) State the intervals on which f is increasing and those on which it is decreasing.