1- find the minimum (x ∗ ∗ ) ) of: ) = −x 3 + 3 4 x 4 a) using the golden search method. a. (20 points) assume = 0.5 and start from ) to bracket the minimum. b. (20 points) after the minimum is bracketed, manually perform 3 steps of the golden section search and report the values of ,), ), ), at each step.

Describe one experiment in which the glass transition temperature and melting temperature of a totally amorphous thermoplastic material can be determined. show the relevant experimental results in a diagram which should be properly annotated with the two temperatures clearly marked. what is likely to happen to the curve in the diagram if the amorphous polymer is replaced by a thermosetting type?