Let be the polynomial function f(x)=2x^ 4 -16x^ 2 +24
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Let f be the polynomial function
f(x)=2x4−16x2+24.
Respond to the following prompts.
(a) Calculate f′(x).
(b) Determine all critical points of f.
(c) Construct a sign chart for f′(x) and state the intervals on which f is increasing and the intervals on which it is decreasing.
(d) Classify each critical point as the location of a local maximum, a local minimum, or neither. Provide justification based on your sign chart.