Remember that a minimizer is not necessarily unique.

[forumfann]

Let
$$f(x):=\frac{1+(1+x)^{4}+(1-2x)^{4}}{\sqrt[4]{1+x^{4}}}$$
and $$x_{0}$$ be the minimizer of $$f(x)$$.
Is it true that
$$x_{0}$$ is the maximizer of
$$g(x):=\frac{1+(1+x)(1+x_{0})^{3}+(1-2x)(1-2x_{0})^{3}}{\sqrt[4]{1+x^{4}}}?$$

Thanks in advance for any helpful answer.

 

[Mark44]

Let
$$f(x):=\frac{1+(1+x)^{4}+(1-2x)^{4}}{\sqrt[4]{1+x^{4}}}$$
and $$x_{0}$$ be the minimizer of $$f(x)$$.
Is it true that
$$x_{0}$$ is the maximizer of
$$g(x):=\frac{1+(1+x)(1+x_{0})^{3}+(1-2x)(1-2x_{0})^{3}}{\sqrt[4]{1+x^{4}}}?$$

Thanks in advance for any helpful answer.

extreminizer?? I've never seen that word before.

It's given that x₀ is the minimizer of f, which means that f(x₀) <= f(x) for all x in the domain of f.

What can you say about g(x₀)? You might want to compare f(x₀) and g(x₀).