Answer
Step 1: $y=x^4$.
Step 2: $x=-3,-1,1$, $f(0)=3$,
Step 3: $x=-3,-1$ (multiplicity 1, crosses the x-axis), $x=1$ (multiplicity 2, touches the x-axis).
Step 4: $3$
Step 5: See graph.
Work Step by Step
Step 1: For $f(x)=(x-1)^2(x+3)(x+1)$, we can determine the end behavior of the graph as similar to $y=x^4$.
Step 2: We can find the x-intercept(s) (let $y=0$) $x=-3,-1,1$, y-intercept(s) (let $x=0$) $f(0)=3$,
Step 3: We can determine the zero(s) $x=-3,-1$ (multiplicity 1, crosses the x-axis), $x=1$ (multiplicity 2, touches the x-axis).
Step 4: We can determine the maximum number of turning points $n-1=4-1=3$
Step 5: See graph.
