MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f(x)=x4−4x3+10 for all real x.
(a) Obtain f′(x) and hence find all critical points.
(b) Construct a sign table for f′(x) showing its sign in each interval determined by the critical points.
(c) Classify every critical point identified in part (a) as a point of local maximum, local minimum or neither. State the corresponding value of f at each such point.
(d) State the intervals on which f is strictly increasing and those on which it is strictly decreasing.