suppose that f(x) = x^3 x<=1
ax+b x>1
is differentiable at x=1 then a=?, b=?
slope of f(x)=2x^2 at x=1 slope=2
slope of g(x)=a+b at x=1
f(1)=1
g(1)=a+b
so for g(1)=f(1), AND f'(1)=g'(1) then
a+b=1 and
a+b=2
Hmmm. not possible, so the conclusion is....