Write MATLAB scripts to solve problem 5.21 from the textbook (bisection, specific heat) four times:

a) with the bisection method (starting interval [0, 1200])

b) with the false-position method (starting interval [0, 1200])

c) with the Newton-Raphson method (x0 = 0)

d) with the secant method ((x0, x1) = (0, 1))

use percent relative error = 10^-6 as stopping criterion.

5.21-Mechanical engineers, as well as most other engineers, use thermodynamics extensively in their work. The following polynomial can be used to relate the zero-pressure specific heat of dry air c_p kJ/(kg K) to temperature (K):

c_p = 0.99403 + 1.671 10^?4T + 9.7215 10^?8T² ?9.5838 10^?11T³ + 1.9520 10^?14T ⁴

Develop a plot of c_p versus a range of T = 0 to 1200 K, and then determine the temperature that corresponds to a specific heat of 1.1 kJ/(kg K).