Sydney Grammar 2009 help (1 Viewer)

mathpie

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I've attached the question I don't understand. specifically, I don't understand the 3rd line of the solution, which states there is a double root at the y-coordinates of the stationary points? is that a rule where y-f(x) = 0 has a double root at y=f'(x)??
 

peter ringout

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Nice question
Just use the formula in a) with p=3 to yield q=plus or minus 2
This means that y=x^3-3x+2 and y=x^3-3x-2 both have double roots....ie max or min situated at the x axis
Sliding y=x^3-3x+2 down 2 units gives a stationary point for y=x^3-3x with a y-value of -2. Similarly for the other
 

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