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.

Determine (a) the maximum thermal efficiency of reversible power cycles operating between a hot reservoir at 1000°c and a cold reservoir at 200°c and (b) the maximum cops for reversible refrigeration and heat pump cycies, respectively, between 28°c and 14°c.

Plot schematically the tensile stress versus strain curves for a typical thermoplastic material at a temperature below its glass transition temperature (tg and at a temperature above its tg, respectively. do the same for a typical thermosetting material. list in a table any differences or similarities between the two materials at t> tg and t < tg, respectively, and relate them to the structures of the two types of polymers

Aheat pump that operates on the ideal vapor compression cycle with refrigerant-134a is used to heat water from 15°c to 45°c at a rate of 0.12 kg/s. the condenser and evaporator pressures are 1.4 and 0.32 mpa, respectively determine: (a) the power input to the heat pump