the coordinate of statianary point of the given function y=x^2_4x

To find the coordinates of stationary points of the function y = x^2 – 4x, we need to first find the derivative of the function and then set it equal to zero to find the critical points. The critical points correspond to the stationary points of the function.

y = x^2 – 4x y’ = 2x – 4

Setting y’ equal to zero, we get:

2x – 4 = 0

Solving for x, we get:

2x = 4

x = 2

Therefore, the critical point (and the stationary point) of the function is at x = 2.

To find the corresponding y-coordinate, we substitute x = 2 back into the original function:

y = x^2 – 4x y = 2^2 – 4(2) y = 4 – 8 y = -4

Therefore, the coordinates of the stationary point of the function y = x^2 – 4x are (2, -4).