$(5$ marks$)$ Given the function

$f(x)=x^4-4x^3-11x^2+30x$

a$)$ use an $x-$interval of $0\mathrm{.}0001$ to determine $($estimate$)$ the instantaneous rate of change of the function at $x=1.$ Show your work $($the difference quotient$)$ and give your answer to the nearest tenth. Using a derivative here will result in $0$ marks. $(2$ marks$)$

b$)$ Determine, using calculations similar to part a$,$ whether the function $f(x)$ has a maximum or minimum at the point $x=1.$ Be sure to justify your answer. Using a derivative or second derivative here will result in $0$ marks.

$(3$ marks$)$