∗Now suppose f :
→ ℝ is continuous and differentiable on and
f = 0
f = 1
. Show there are distinct points
i=1n ⊆ such that
−1 = n.Hint: Let 0 = t0 < t1 <
< tn = 1 and pick xi ∈ f−1
such that these
xi are increasing and xn = 1,x0 = 0. Explain why you can do this.
Now choose the ti to be equally spaced.