In this question, for the sake of simplicity, let’s not allow both a and b to be 0.
explanation 1:
We see 2=f” is >0 for all x, but f decreases over -infinity to 0. So f doesn’t have to be increasing because f”>0 for all x. On the other hand, f’ (green curve) is increasing for all x first by becoming less negative and then by becoming positive.
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