Find all lines that are tangent to the curve y = x^3 and are also parallel to the line 3x - y = 5

Any help will be appreciated!

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- March 12th 2008, 08:20 AMhasanbalkanTangent and parallel lines
Find all lines that are tangent to the curve y = x^3 and are also parallel to the line 3x - y = 5

Any help will be appreciated! - March 12th 2008, 08:42 AMwingless
Firstly,

The lines must be parallel to 3x-y = 5, . So their slope must be .

Let our line be , m is the slope and C is a constant. As it'll become

At the tangent point, the line must satisfy .

So the line passes the points (-1,f(-1)) and (1,f(1)).

(-1,-1), (1,1)

The line is

And it makes for (-1,1)

and for (-1,1)

The lines are then

and

*bu arada, türk müsün? =)*