Let $f(x)=(x-21{)}^{\frac{7}{9}}$

Find the critical points $c$ that correspond to local minima.

$($Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if there are no critical points.$)$

Find the critical points $c$ that correspond to local maxima.

$($Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if there are no critical points.$)$

$c$

Find the values at which the points of inflection occur.

$($Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if there are no inflection points.$)$

Determine the interval on which $f$ is concave up$.$

$($Use symbolic notation and fractions where needed. Give your answer as interval in the form $(**,**).$ Use the symbol $$ for infinity, $u$ for combining intervals, and an appropriate type of parenthesis $"(",")","[","]"$ depending on whether the interval is open or closed. Enter $\frac{O}{?}$ if the interval is empty.$)$

xin

Determine the interval on which $f$ is concave down.

$($Use symbolic notation and fractions where needed. Give your answer as interval in the form $(**,**).$ Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis $"(",")",$ "I", "I" depending on whether the interval is open or closed. Enter $\frac{O}{?}$ if the interval is empty.$)$