Question

The values of x for which the function

f(x)=x3+3x2−9x−7 is increasing

Answer 1

Answer:

f(x) is increasing for x>1 or x<-3 .

Step-by-step explanation:

The function is , f(x)= x^3 +3x^2 -9x-7

Then, f'(x) = 3x^2 + 6x -9

The function f(x) will be increasing if f'(x)>0

Now , if f'(x)>0 then, 3x^2 +6x -9>0 => x^2 +2x-3 >0 => (x+3)(x-1) >0

Then, either, (x+3)>0 and (x-1)>0 => x>-3 and x>1 => x>1

Or, (x+3)<0 and (x-1)<0 => x<-3 and x<1 => x<-3

Hence, f(x) is increasing for x>1 or x<-3