Sum of convex and concave function can have non global minima So I just read that the sum of a convex with a concave function is neither convex nor concave in the general case. This would imply that I should be able to find two functions $a(x)$ and $b(x)$ of which one is convex and the other one concave such that a third non convex function $c(x) = a(x) + b(x)$ has at least two local minima of which only a single one is the global one. This would obviously increase the difficulty of our optimization problem as we can not be certain anymore that any local minimizer is the global one. However I can not come up with an example of $a(x)$ and $b(x)$, could somebody share some insights?

Thank you!
Hints:

$-f(x)$ is concave when $f(x)$ is convex

$x^{2n}$ is convex for $n \in \mathbb{N}^+$

$f(x + a)$ has the same convexity as $f(x)$ for $a \in \mathbb{R}$
Hints:

$-f(x)$ is concave when $f(x)$ is convex

$x^{2n}$ is convex for $n \in \mathbb{N}^+$

$f(x + a)$ has the same convexity as $f(x)$ for $a \in \mathbb{R}$