Question

1. f(x)=-x^{3}+1+3x

x - intercepts:
positive interval:
negative interval:

Explanation:

Step1: Find the x - intercepts

The x - intercepts are the points where \(y = f(x)=0\). By looking at the graph, the curve crosses the x - axis at \(x=-1\), \(x = 0\), and \(x = 1\).

Step2: Determine the positive interval

The function \(y=f(x)\) is positive (above the x - axis) when \(x\in(0,1)\).

Step3: Determine the negative interval

The function \(y = f(x)\) is negative (below the x - axis) when \(x\in(-\infty,0)\cup(1,\infty)\).

Answer:

• X - intercepts: \(x=-1\), \(x = 0\), \(x = 1\)
• Positive Interval: \((0,1)\)
• Negative Interval: \((-\infty,0)\cup(1,\infty)\)