Question

Find the maxima and minima of the function

f(x)=x^3-6x^2+9x+15

Answer 1

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) > 0

 

 

              +                                                    _                                        + 

<----------------------|----------------------|-------------------->

 - infinity              1                        3                     + infinity

 

=>   In the interval -infinity < x < 1  and (union)    3 < x < +infinity f(x) is increasing

 

and    in the interval  1 < x < 3  , f(x) is decreasing Answer