Question

find the intervals in which the function is given by f(x)=2x3-21x2+36x-40 a) strictly increasing b) stictly decreasing​

Answer 1

Answer:

f(x) = 2x³ - 21x² + 36x -40

f'(x) = 6x² - 42x + 36 = 6 ( x -1 ) ( x - 6 )

therefore, f'(x) = 0

6 ( x -1 ) ( x - 6 ) = 0 , we get x = 1 , 6

these points divide the real line in 3 intervals such as

( - ∞, 1 ) , ( 1 , 6 ) , ( 6 , ∞ )

three cases arises

case 1 :- Interval ( - ∞, 6 )

f'( x) > 0

f ( x) strictly increasing

case 2 :- interval ( 1 , 6 )

f' (x) < 0

f (x) Strictly decreasing

case 3 :- interval ( 6 , ∞)

f' (x) > 0

f (x) strictly increasing