Final answer:
To find the stationary points of the function f(x) = 2x^3 + 3x^2 - 12x + 4, we differentiate the function and solve for x when the derivative equals 0.
Step-by-step explanation:
The given function is f(x) = 2x^3 + 3x^2 - 12x + 4. To find the stationary points, we need to find the values of x where the derivative of the function equals 0.
To find the derivative of f(x), we differentiate each term and set it equal to 0:
f'(x) = 6x^2 + 6x - 12 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± √(b^2 - 4ac))/(2a)
Substituting the values a = 6, b = 6, and c = -12, we get x = -2 and x = 1.
Therefore, the stationary points are x = -2 and x = 1.