MATH 1ZB3 Lecture 6: complex-lecture6.6

1. P(x) is a polynomial of degree 4, e. P(z) PrPpr+p such that P(5)-521. F"(5)-434. P"(5)=272. P"(5)=1 14. Far"(5)=24. a) Find the coeficients po P Pa Ps Ps b) Write the expansion of P(r) in powers of (r 1)

Compute Ps(r) for f(z) = cos( 2) around a = 0.

Consider the function f(z,y)(2) 3) on the compact set D R2 : ф(x, y) 0), where p(z, y)-x2 + y2-18. (, y) E 1) Show that the candidate extrema of f on the boundary of D are given by 乃= (0,-3/2), Pı = (0.3V2), P = (-3,3), Po = (3, 3)乃= (-V17,-1), Ps (V17,-1). 2) Show that Ps is a global maximum for f on D, while P and Ps are global minima for f on D.