Final answer:
To find the absolute minimum value of h over the closed interval -3 <= x <= 2, we need to find the x-value where the derivative of h(x) is equal to zero.
Step-by-step explanation:
The absolute minimum value of h over the closed interval -3 <= x <= 2 occurs at the x-value where the derivative of h(x) is equal to zero. To find this x-value, we need to find the derivative of h(x) and find the critical points.
First, find the derivative of h(x) by applying the power rule: h'(x) = 6x² + 6x - 12.
Next, set the derivative equal to zero and solve for x: 6x² + 6x - 12 = 0.
Finally, use methods such as factoring, completing the square, or the quadratic formula to solve for the x-values. The x-value where the absolute minimum occurs is the value that gives the smallest value for h(x) over the interval -3 <= x <= 2.