HW 16, due Thursday, October 27, 11:59:00 pm 40. (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and inflection points of f. (d) Sketch the graph of f with the information you found in (a)(c), and check your sketch on a graphing device. f(t) : t+cos(t), ~27r 5 t 5 2w Section 4.4 52. Sketch the graph of a function which satisfies all the conditions below. f' (2) = 0, f'(0) = 1, f'(x) > 0 if0 2, f" (x) 0 if x> 4, lim f (x) = 0, f(-x) =-f(x) for all xSection 4.5 40. In the theory of relativity, the energy of a particle is h2C2 E=ilmc4+ A2 where m0 is the rest mass of the particle, A is the particle's wave length, and h : h is Planck's constant. Sketch the graph of E as a function of A; mg c4 and h2 c2 are constants. What does the graph say about energy as wavelength changes