MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The function h(x)=x5−5x3+4x is defined for all real numbers.
(a) Determine every critical point of h(x).
(b) For each critical point, decide whether it corresponds to a local maximum or a local minimum.
(c) Compute the function values at all critical points and arrange these values in descending order of magnitude.
(d) State which extremum has the greatest magnitude and which has the smallest magnitude (closest to zero).