Question

6. y = x (x - 3)2 decreases for the 1 point values of x given by
​

Answer 1

Answer:

We have, y=x(x−3)

2

∴

dx

dy

=x2(x−3).1+(x−3)

2

.1

=2x

2

−6x+x

2

+9−6x=3x

2

−12x+9

=3(x

2

−3x−x+3)=3(x−3)(x−1)

So, y=x(x−3)

2

decreases for (1,3).

[since, y

′

<0 for all Xxϵ(1,3), hence y is decreasing on (1,3) ]