Question

find the interval on which the function f(x)=x²+5x²+8x+1 is a strictly increasing function​

Answer 1

Answer

Wehave,f(x)=

4

x

4

−x

3

−5x

2

+24x+12

⇒f

′

(x)=x

3

−3x

2

−10x+24

⇒f

′′

(x)=3x

2

−6x−10

Iff

′′

(x)>0thefunctionisstrictlydecreasingandiff

′′

(x)<0

⇒3x

2

−6x−10=0

⇒x=

6

6±

36+4×3×10

=

6

6±

156

=

6

6±12.4899

⇒x=3.08or−1.08

Wegetthatf

′′

(x)<0when−1.08<x<3.08andf

′′

(x)>0whenx>3.08andx<−1.08

∴f(x)isstrictlyincreasingwhen−1.08<x<3.08

andf(x)isstrictlydecreasingwhenx>3.08andx<−1.08