Question

How do you find the equation of the line that is tangent to `f(x)=x^3` and parallel to the line `3x-y+1=0`?

Answer 1

`y=3x+-2`

Explanation:

The tangent in `x_0` must have `m=f^'(x_0)=3x_0^2` and at the same time be parallel to `y=3x+1 => m=3`
so
`x_0^2=1`
and
`x_0=+-1 => y_0=+-1`
the tangent equation is
`(y-y_0)=3(x-x_0)`
`(y+-1)=3(x+-1)`
`y=3x+-2`