Answer: (0,0) and (3,-27)
Step-by-step explanation:
Given
Function is [tex]y=x^4-4x^3[/tex]
The stationary point on the graph are the points where the function is neither increasing nor decreasing i.e.
[tex]\Rightarrow \dfrac{dy}{dx}=4x^3-4\times 3x^2\\\\\Rightarrow \dfrac{dy}{dx}=4x^3-12x^2=0\\\\\Rightarrow 4x^2(x-3)=0\ \text{i.e.}\\\\\Rightarrow x=0\ \text{or}\ 3[/tex]
Values of y corresponding to it is
[tex]\text{for x=0},\ y=0\\\text{for x=3},\ y=3^4-4\times 3^3=-27[/tex]
