AMAT $112$ Calculus $1$

Written Assignment $3$

Question $3)$ Using the following information, determine all intervals of increasing and decreasing, x $-$ and y $-$intereepts, local maximums, local minimums, intervals of concave up$,$ intervals of concave down, and inflection points. Then, using this information, graph your function. Do not use a graphing calculator or tool. $(12$ points$)$

$f(x)=(x-1)(x-4{)}^2$

$f^{\text{'}}(x)=3(x-2)(x-4)$

$f^{\text{'}\text{'}}(x)=6x-18$