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Show that the function x 3 - 3x -5 has exatly one root for x belongong to (0,5)

Show that the function x3 - 3x -5 has exatly one root for x belongong to (0,5)

Grade:12

1 Answers

Pratham Ashish
17 Points
12 years ago

hi,

 let f = x3 - 3x -5 

f(0) = -5  & f ( 5 ) = 105

df/dx = 0  @ x=1

 function is decrasing in (0,1 ) & increasing in (1,5 ) .   it will lie below the x axis in (0,1) & will cross the x-axis only once in (1,5 ) , since it is strictly increasing in this region, so there will be only one root

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