Question

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

Answer 1

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

Step-by-step 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 $(0,0), (3,-27)$