Question

Find the interval off following function either increasing or decreasing F(x)=(x-1) (x-2)^2​

Answer 1

Answer:

increasing

Step-by-step explanation:

iam thinking

Answer 2

Answer:

f(x)=x

x

Now taking y=x

x

(∵y=f(x))

∴logy=xlogx

Now differentiate w.r. to x

∴

y

1

dx

dy

=x(

x

1

)+1⋅logx

∴

dx

dy

=y(1+logx)

=x

x

(1+logx)

Hence f(x)=x

x

(1+logx)

Now, f(x) is decreasing function.

∴f

′

(x)<0

∴x

x

(+logx)<0

∴1+logx<0

∴logx<−1

∴x<e

−1

∴x<

e

1

∴x∈(0,

e

1

) function f(x)=x

x

is decreasing function.