$f(x)=x^{4}ln(x)$

$($a$)$ Graph the function.

$(1)$

$($b$)$ Use T'Hospital's Rule to determine the limit as $x{0}^{+}.$

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$0$

$($c$)$ Use calculus to find the minimum value.

$\frac{-1}{4e}$

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Find the interval where the function is concave up$.($Enter your answer in interval notation.$)$

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$(e^{(\frac{-2}{3})},)$

Find the interval where the function is concave down. $($Enter your answer in interval notation.$)$

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