Question

find second derivative of
f(x)= x²log|cosx|​

Answer 1

।।।।।।।।।।।।।।।।।।।।।।।।।।।।।।।।।

Answer 2

f(x)=cosx

f

′

(x)=−sinx

(i)x∈(0,π)

⇒sinx>0⇒−sinx<0

⇒f

′

(x)<0

so f(x) is strictly decreasing on (0,π)

(ii) x∈(π,2π)⇒sinx<0

⇒−sinx>0

⇒f

′

(x)>0

so f(x) is strictly increasing on (π,2π)

(iii) As f

′

(x)<0 for x∈(0,π)

and f

′

(x)>0 for x∈(0,2π)

Hence f(x) is neither increasing nor decreasing on (0,2π).