Question

Hii
Good morning everyone
Class 12 question exercise 6.2

please solve the question

find the value of x for which y={x(x-2)}^2
is an increasing function​

Answer 1

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1. HOPE IT HELP YOU

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please yar

Answer 2

Hey mate...

y = {x(x - 2)}²

differentiate with respect to x,

dy/dx = 2{x(x - 2)} [x. d(x -2)/dx + (x -2).dx/dx ]

= 2{x(x - 2)} [x + x - 2 ]

= 4x(x - 2)(x - 1)

So, the points x = 0, x =1 and x = 2 divides the real line into four disjoint intervals,

(-∞,0), (0,1), (1, 2) and (2,∞).

for increasing , dy/dx > 0

4x(x - 1)(x - 2) > 0

see attachment ,we get ,

x ∈ (0, 1) U (2, ∞)

Hope helps....