Consider the one-parameter family of continuous functions fp(x)=x3−3x+p. A student plans to locate a real zero by repeatedly halving the interval [0,2]. For which of the following values of the parameter p is this strategy guaranteed to capture a zero inside (0,2)?
a) p<−2
b) p∈(0,2)
c) p∈(−2,0)
d) p∈(−2,2)