4. Suppose that f: R2 ---t R is CP on Br(xo, Yo) for some r > O. Prove that given (x, y) E Br(xo, yo), there is a point

(c,

d) on the line segment between

(xo, yo) and (x, y) such that f(x,y) = f(xo,yo)

p-1 1 (k (k) . . f}k f )

+ L k! L . (x - xo)1 (y - YO)k-) f}x j f} k-j (xo, Yo)

k=l j=O J Y

+ -1, LP (p.) (x - Xo )j( Y - Yo )P_j >:>.f }P>:> f _. (cd, ) .

p.. J UX) uyP )

)=0