Let f(x)=x3−5x+2.
(a)–(c) below refer to the interval [1,2].
a. Calculate f(1) and f(2).
b. Determine whether f has a real zero in (1,2). Provide justification for your conclusion.
c. If your answer to part (b) is affirmative, identify a subinterval of length 21 contained in (1,2) that must also contain a zero of f. Show how you obtained the subinterval.