Question

9x+6x2-x3. Find incresing and decreasing interval

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

❤ Hello ❤

Step-by-step explanation:

▶ INCREASING ⤵

$- {x}^{3} + 6 {x }^{2} + 9x$

Hope it's help u