Final answer:
To find the points where the tangent line is horizontal for the given function f(x)=x³−4x²+ 2, we need to find the critical points where the derivative of the function is equal to zero.
Step-by-step explanation:
To find the points where the tangent line is horizontal for the given function f(x)=x³−4x²+ 2, we need to find the critical points where the derivative of the function is equal to zero.
To do this, we take the derivative of the function f(x) and set it equal to zero. Then, we solve for x to find the x-coordinates of the critical points.
Finally, we substitute the x-coordinates back into the original function to find the corresponding y-coordinates of the points where the tangent line is horizontal.