Question

In which interval is the function f(x)=x^3+6x^2+9x+1 increasing?

Answer 1

Answer:

Answer : Given : f(x) = x3 - 6x2 +9x +15

To find : the interval in which f(x) is increasing or decreasing

 

 

Now  

f(x) = x3 - 6x2 +9x +15

f `(x) = 3x2 - 12x + 9 = 3 (x2 - 4x + 3 )  

 

for f(x) to increase

f `(x) > 0  

=>  3 (x2 - 4x + 3 ) > 0

=> x2 - 4x + 3  > 0

=> (x - 3) ( x - 1) >

Step-by-step explanation:

Answer 2

Please see the attachment