Final answer:
The inequality x² - 8x + 15 < 0 has the critical points 3 and 5, which are the solutions to the equation x² - 8x + 15 = 0. The inequality holds true for the interval 3 < x < 5.
Step-by-step explanation:
To solve the inequality x² - 8x + 15 < 0, we first need to find the roots of the corresponding quadratic equation x² - 8x + 15 = 0. We can factor this equation as (x - 5)(x - 3) = 0, thereby finding the roots to be x = 3 and x = 5. These roots represent the critical points where the sign of the inequality can change.
Next, we test values around the critical points to determine the intervals where the inequality holds true. The three intervals to test are x < 3, 3 < x < 5, and x > 5. Through testing, we can find that the inequality x² - 8x + 15 < 0 holds true for the interval 3 < x < 5, meaning the solution set is between the critical points 3 and 5.
Looking at the answer choices, the critical points for the inequality given are Option C: 3 and Option D: 5.