Question

cy find the sol set,
4 12x-1) 22 (1-2x),xel​

Answer 1

Answer:

Given,

f(x)=2x

3

+9x

2

+12x−1

differentiate with respect to x , we get

f

′

(x)=6x

2

+18x+12

For the critical points put f

′

(x)=0

i.e. 6x

2

+18x+12=0

6(x

2

+3x+2)=0

(x+2)(x+1)=0

x=−2,x=−1

Clearly, f

′

(x)>0 if x<−2&x>−1

f

′

(x)<0 if −2<x<−1

Thus f(x) increases in (−∞,−2)∪(−1,∞), decreases in (−2,−1)