Calculate the coordinates of the stationary points of the following function: � ( � ) = 0.5 � 4 − 4 � 2 f(x)=0.5x 4 −4x 2

To find the stationary points of the function f(x) = 0.5x^4 - 4x^2, we first need to find the derivative of the function.

The derivative of f(x) = 0.5x^4 - 4x^2 is f'(x) = 2x^3 - 8x.

Next, we set the derivative equal to zero and solve for x to find the x-coordinates of the stationary points:

2x^3 - 8x = 0 x(2x^2 - 8) = 0 x = 0 or x = ±sqrt(4)

So, the x-coordinates of the stationary points are x = 0, x = 2, and x = -2.

To find the y-coordinates of the stationary points, we substitute these x-values back into the original function:

f(0) = 0.5(0)^4 - 4(0)^2 = 0 f(2) = 0.5(2)^4 - 4(2)^2 = -4 f(-2) = 0.5(-2)^4 - 4(-2)^2 = -4

So, the stationary points of the function are (0, 0), (2, -4), and (-2, -4).