The equation: x^3 - 12x + 6 has two turning points. Use calculus to find the positions and natures of these turning points.

To find the turning points we need to find when the differential of the equations with respect to x is equal to 0. (dy/dx = 3x² - 12 = 0) From this we find that the turning points happen when x = 2, x = -2 Sub this back into the equation of f(x) and we get that the coordinates of the turning points are (2, -10) and (-2, 22) Now to find the nature of these turning points we need to find the values of the second defferential of f(x) (d²y/dx² = 6x) So at the two turning points the second differentials are equal to 12 and -12 respectively. Therefore the point (2, -10) is a minimum because 12 is more than 0 and the point (-2, 22) is a maximum because -12 is less than 0.