Determine the points of continuity for the function f:R to R defined by f(x) = 2x if x is rational and f(x) = x+ 3 if x is irrational . With proof.

f: [-5,5]→[3,18] Surjective & differentiable f

g(x) = f(x) f'(x) Twice differentiable fr

g(0)=k Find least integral value of k such that there always exists some CEES✓ f" to satisfy (f' * (c)) ^ 2 =-f(c)f^ prime prime (c) \&(f(c))^ 2 f^ prime prime (c) < 3 * (f' * (c)) ^ 3