Question

Find the values of x for which y = [x(x – 2)]² is an increasing function.

Answer 1

Answer:

Hola!............ ❤

We have:

f(x)=[x(x−2)]^2

⇒f(x)=x^2(x−2)^2

Differentiating both sides with respect to x we get,

f'(x)=x^2.d/dx(x−2^)2+(x−2)^2.d/dx(x^2)

=x^2.2(x−2)+(x−2)^2.2x

=2x(x−2)(x+x−2)

=2x(x−2)(2x−2)

⇒f'(x)=4x(x−1)(x−2)

Now, 

f'(x) = 0

⇒4x(x−1)(x−2)

⇒x = 0, 1, 2

So, f' is increasing on (0, 1) ∪ (2, ∞)

Hope it’s helpful........ ☺