Answer
(a) $-4, -\frac{1}{4}, 2$.
(b) $x=-4, -\frac{1}{4}, 2$, $f(0)=-8$.
(c) local maximum $f(-2.5)=60.75$, local minimum $f(1)=-25$.
(d) See graph.
Work Step by Step
(a) For $f(x)=4x^3+9x^2-30x-8$, use synthetic division as shown to find zero(s) $x=2$. Use quotient to find other zeros $4x^2+17x+4=0\Longrightarrow (x+4)(4x+1)=0\Longrightarrow x=-4, -\frac{1}{4}$.
(b) The intercepts are $x=-4, -\frac{1}{4}, 2$, $f(0)=-8$.
(c) See graph, we can find a local maximum $f(-2.5)=60.75$, a local minimum $f(1)=-25$.
(d) See graph.
