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by direct incpection

x=2.3    $\Rightarrow$   f(x)=1.8

x=2.5    $\Rightarrow$   f(x)=1.6

x=2.7    $\Rightarrow$   f(x)=1.8

now we can check value of f(x) before and after 2.5+$\alpha$, 2.5 - $\alpha$

x=2.5+$\alpha$ $\Rightarrow$  f(x)=1.6+$\alpha$ and

x=2.5-$\alpha$ $\Rightarrow$  f(x)=1.6+$\alpha$

so we can conclude that this is minimum value

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