Question

Y=x+ - 4x3
Find the two stationary points
on the graph of y=x4 - 4x3

Answer 1

Answer:
`(0,0), (3,-27)`

Explanation:

Given

Curve is
`y=x^4-4x^3`

The stationary point on a differentiable function is the points where the differentiation of the function is zero i.e. slope is zero at that point.

Differentiate the curve
`f(x)=x^4-4x^3`

`\Rightarrow f'(x)=4x^3-12x^2`

Equate it to zero

`\Rightarrow 4x^3-12x^2=0\\\Rightarrow 4x^2(x-3)=0\\\Rightarrow x=0,0,3`

Put
`x=0,3` in the function
`f(x)=x^4-4x^3`

`\Rightarrow f(0)=0\\\Rightarrow f(3)=3^4-4(3)^3\\\Rightarrow f(3)=81-108\\\Rightarrow f(3)=-27`

Therefore, the stationary points are
`(0,0), (3,-27)`