Questions: the graph of the polynomial function to solve the inequality. 3x^3 + 14x^2 ≥ 28x + 24 f(x) = 3x^3 + 14x^2 - 28x - 24 The solution set is (-∞, -4] ∪ [-2/3, ∞). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

$the graph of the polynomial function to solve the inequality. 3x^3 + 14x^2 ≥ 28x + 24 f(x) = 3x^3 + 14x^2 - 28x - 24 The solution set is (-∞, -4] ∪ [-2/3, ∞). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)$

Transcript text: the graph of the polynomial function to solve the inequality. \[ 3 x^{3}+14 x^{2} \geq 28 x+24 \] $f(x)=3 x^{3}+14 x^{2}-28 x-24$ The solution set is $(-\infty,-4] \cup\left[-\frac{2}{3}, \infty\right)$. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Solution

Solution Steps

Step 1: Rewrite the inequality

We rewrite the inequality $3x^3 + 14x^2 \ge 28x + 24$ as $3x^3 + 14x^2 - 28x - 24 \ge 0$.

Step 2: Analyze the graph

The graph of $f(x) = 3x^3 + 14x^2 - 28x - 24$ is given. We look for the intervals where $f(x) \ge 0$. This corresponds to where the graph lies on or above the x-axis.

Step 3: Identify the intervals

The graph is on or above the x-axis for $x \le -4$ and $x \ge -\frac{2}{3}$.