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Discussion Response Post to: Maxima Minima Questions

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Swaty gupta (551)

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y = sinx + ax + b

y' = cosx + a

a) if a>1, b<0

so, cosx + a>0 .. (a>1)

therefore y is always increasing. (has only one root)

let for a value of x,

y=0

sinx + ax + b=0,

sinx + ax = -b

sinx + ax > 0 (b<0)

now since a>1, ax > sinx

so ax will decide the sign of expression.. hence the root is positive.

b) a>1 , b>0

has only one root.. (a>1)

and sinx + ax<0, (b>0)

so, root is negative.

c)a<-1, b<0

y' = cosx + a

y' < 0 (a<-1)

so, y is always decreasing. (has only one root)

sinx + ax + b =0 (for some x)

sinx + ax = -b

sinx + ax >0 (b<0)

so, the root is negative.

Sure i am that this day we are the masters of our fate, that the task set before us is not above our strengths; that its pangs and toils are not beyond our endurance. As long as we have faith in our own cause and an unconquerable will to win, victory will not be denied us. - Winston Churchill

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