568. $y=1-\sqrt[5]{(x-2)^{4}}$

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568. $y=1-\sqrt[5]{(x-2)^{4}}$
Solution. $1^{0} . y^{\prime}=-\frac{4}{5}(x-2)^{-1 / 5}=-\frac{4}{5 \sqrt[5]{x-2}}$.

$2^{0}$. The derivative does not become zero for any values of $x$ and does not exist only at $x=2$. This is the critical point.

$3^{0}$. In the interval $(-\infty, 2)$, the derivative is positive, and in the interval $(2, \infty)$, it is negative; therefore, the function has a maximum at $x=2$.

$4^{0}$. We find $f(2)=y_{\max }=1$.