Explanation:
F(x) = 2x³ - 3x + 1.
d/dx [2x³ - 3x + 1] = 6x² - 3.
Firstly, we wish to find the stationary points of F(x).
When 6x² - 3 = 0, x = -0.707 or x = 0.707.
Now we use Second Derivative test:
d/dx [6x² - 3] = 12x.
Since 12(-0.707) < 0, x = -0.707 is a relative maximum point.
Since 12(0.707) > 0, x = 0.707 is a relative minimum point.
Hence x = 0.707. To find the exact point you can substitute the value of x back into the equation 2x³ - 3x +1.