Question Detail
Question
The curve y = 11 - 12x + 6x² - x³ has one of the following:
Correct Answer
Option C is the correct answer.
Detailed Explanation
To find points of inflexion, we need to find the second derivative and set it to zero.First derivative: y' = d/dx(11 - 12x + 6x² - x³) = -12 + 12x - 3x².Second derivative: y'' = d/dx(-12 + 12x - 3x²) = 12 - 6x.Set y'' = 0: 12 - 6x = 0 => 6x = 12 => x = 2.To confirm it's an inflexion point, check the third derivative:y''' = d/dx(12 - 6x) = -6.Since y'''(2) = -6 ≠ 0, x = 2 is indeed a point of inflexion.
Hint
Points of inflexion are found by setting the second derivative to zero and checking the third derivative.