Question

6. Find the value of x : (/)x * (/)2 = (/)6

Answer 1

Answer:

Find the value of x : (/)x * (/)2 = (/)6

Step-by-step explanation:

=[x(x−2)]

2

=[x

2

−2x]

2

∴

dx

dy

=y

′

=2(x

2

−2x)(2x−2)=4x(x−2)(x−1)

∴

dx

dy

=0⇒x=0,x=2,x=1

The points x=0,x=1, and x=2 divide the real line into four disjoint intervals

i.e., (−∞,0),(0,1),(1,2) and (2,∞).

In intervals (−∞,0) and (1,2) ,

dx

dy

<0

∴ y is strictly decreasing in intervals (−∞,0) and (1,2)

However, in intervals (0,1) and (2,∞),

dx

dy

>0.

∴ y is strictly increasing in intervals (0,1) and (2,∞).

∴ y is strictly increasing for 0<x<1 and