Question

Find the interval on which f(x)=2log(x-3)-x^2+6x+1 is an increasing function

Answer 1

Answer:

Step-by-step explanation:

Correct option is

A

(3,4)

f  

′

(x)=  

x−3

2

​

−2x+6=  

x−3

2

​

−2(x−3)=2.  

x−3

1−(x−3)  

2

 

​

 

⇒f  

′

(x)=−2.  

x−3

x  

2

−6x+8

​

=−2.  

x−3

(x−2)(x−4)

​

 

For f(x) to be increasing, f  

′

(x)>0

⇒  

x−3

(x−2)(x−4)

​

<0⇒x∈(−∞,2)∪(3,4)

Also for log(x−3) to be defined x−3>0⇒x>3

Hence interval of increasing is (3,4)

make me a brainlest

Answer 2

Answer:

x= ( 2,4 )

Step-by-step explanation:

f'(x) > 0

2/x-3 -2x +6 >0

2-2x^2 + 6x + 6x - 18/x-3 > 0

x^2 -6x +8 < 0

(x-2)(x-4) < 0

x = (2,4)