f(x) = Exp[x^2 - 1] + 10 Sin[2 x] - 5

f'(x) = 2 Exp(-1 + x^2) x + 20 Cos[2 x]

f''(x) = 2 Exp(-1 + x^2) + 4 Exp(-1 + x^2) x^2 - 40 Sin[2 x]

Here you can see both f(x) and f''(x) as blue and violet.

One of the convergence conditions is that either f''(x) <= 0 or f''(x) >= 0 in [a,b]. But I don't seem to find any [a,b] where there is a zero on f(x) and also f''(x) <= 0 or f''(x) >= 0. What is the flaw here? Or it really isn't possible?

Any clue?