Thread: Tangent 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!

Originally Posted by hasanbalkan

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!

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? =)