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