Question

Find the intervals in which the function f(x)=15-9x+6x^2-x^3 is increasing,decreasing.

Please answeer fast...

Answer 1

Answer:

Step-by-step explanation:

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

image

⇒ 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

Answer 2

Answer:

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