Suppose f C[a, b], that x1 and x2 are in [a, b]. a. Show that a number exists between x1 and x2 with

Suppose f ˆˆ C[a, b], that x1 and x2 are in [a, b].
a. Show that a number ξ exists between x1 and x2 with

b. Suppose that c1 and c2 are positive constants. Show that a number ξ exists between x1 and x2 with

c. Give an example to show that the result in part b. does not necessarily hold when c1 and c2 have opposite signs with c1 ‰  ˆ’c2.

f (xi) +f(r2) I 21) f()= f (x1 ) + cif(x) cf(x2)