MAT $421$

QUESTION $3$

Given the function $f(x)=3x^2-x^3.$

a$)$ Find the $x-$intercept and $y-$intercept of $f.$

b$)$ Find the interval$($s$)$ where $f$ is increasing and decreasing. Hence, determine the relative

extremum of $f($if any$).$

$(7$ marks$)$

c$)$ Find the interval$($s$)$ where the function is concave up or concave down. Hence, determine

the inflection point$($s$)($if any$).$

$(7$ marks$)$

d$)$ Sketch the graph of $f$ by using the information above.