391)
http://mathworld.wolfram.com/IncreasingFunction.html
Doubt 1 : What is an increasing function ?
Doubt 2 : If b>a then the eqn. (x-a)(x-b)-1=0 has
A. both roots in [a,b]
B.both roots in (-∞,a)
C. both roots in (b,+∞)
D. One root in (-∞,a)and the other in (b,+∞)
Doubt 3. Let -1≤p≤1
Show that the equation 4x3-3x-p=0 has a unique root in the interval [1/2,1] and identify it.
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3 Answers
62Question 2,
think of the parabola (x-a)(x-b)
it will cut the x axis at a,b
when you subtract 1, you will pull the parabola down...
so both roots will be outside the interval [a,b]
62when you use x=cos theta,
you get cos 3 theta==p
now try to finish the proof :)
