SOLVED:Given a continuous function f on an interval I, prove-using ordinary integration of functions - that there exists a unit-speed curve β(s) in 𝐑^2 for which f(s) is the plane curvature. (Hint: Reverse the logic in Ex. 8 of Sec. 2.3.)

Prove that if f is continuous real valued function on theinterval [0, 1] such that f(0)f(1) 0. Let A = x ∈ [0, 1] :f(x) ≥ 0. Then A is non-empty and bounded.Don't use Intermediate value theorem

What does it mean for a function to be continuous on an interval? | Study Prep in Pearson