Question

(ii) Find the two stationary points on the graph of
y = x^4 – 4x^3.

I’ll be thankful if someone answers I’ve a deadline to meet

Answer 1

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

Step-by-step explanation:

Given

Function is  $y=x^4-4x^3$

The stationary point on the graph are the points where the function is neither increasing nor decreasing i.e.

$\Rightarrow \dfrac{dy}{dx}=4x^3-4\times 3x^2\\\\\Rightarrow \dfrac{dy}{dx}=4x^3-12x^2=0\\\\\Rightarrow 4x^2(x-3)=0\ \text{i.e.}\\\\\Rightarrow x=0\ \text{or}\ 3$

Values of y corresponding to it is

$\text{for x=0},\ y=0\\\text{for x=3},\ y=3^4-4\times 3^3=-27$