Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. f(x)=9xe^x Increasing: a) (-oo,-1) b) (-1,oo) c) (-oo,0) d) (-oo, oo) e) (0, oo) f) no interval

blackdivcp

blackdivcp

Answered question

2022-10-29

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.
f ( x ) = 9 x e x
Increasing:
a) ( , 1 )
b) ( 1 , )
c) ( , 0 )
d) ( , )
e) ( 0 , )
f) no interval

Answer & Explanation

Milton Hampton

Milton Hampton

Beginner2022-10-30Added 16 answers

f ( x ) = 9 x e x f ( x ) = 9 x e x + e x ( 1 ) f ( x ) = 9 e x ( x + 1 )
Put f'(x) = 0
9 e x ( x + 1 ) = 0 ( x + 1 ) = 0 x = 1
if x > - 1 then f'(x) > 0
So f(x) is increasing when x > - 1 or ( 1 , )
If x < - 1 then f'(x) < 0
So f(x) is decreasing when x < - 1 or ( , 1 )

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