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find the intervals on which the functions are increasing and decreasing? 1.f(x)=(x+1)^3 (x-3)^2 ?

find the intervals on which the functions are increasing and decreasing?
1.f(x)=(x+1)^3 (x-3)^2 ?

Grade:11

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
df/dx=(x+1)^3.2(x-3)+(x-3)^2.3(x+1)^2
=(x+1)^2(x-3)[2(x+1)+3(x-3)]
=(x-3)[2x+2+3x-9]
=(x-3)(5x-7)
for function to be increasing df/dx>or=0
(x-3)(5x-7)>or =0
x<or=7/5 or x>or=3
i.e. (-infinity,7/5]U[3,infinity)

for function to be decreasing df/dx<0
(x-3)(5x-7)<0
7/5<x<3

Thanks & Regards
Rinkoo Gupta
AskIItians Faculty

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