Let a,b ∈ R with a < b and f : [a,b] → [a,b] be a continuous and differentiable function on (a,b). Show that if f′(x) ̸= 1 for all x ∈ (a,b), then there exists a unique p ∈ [a,b] such that f(p) = p. Prove using the intermediate value theorem