Find equation of line f(x) parallel to given line
This is another one of those problems that I kinda get the idea of how to do it but then just can't think of anything else. So, to the problem.
Function
$\displaystyle
f(x) = x^3
$
$\displaystyle f'(x) = 3x^2 $
Line
$\displaystyle
3x-y+1 = 0
$
$\displaystyle y = 3x+1$
From here we know that $\displaystyle m=3$ since $\displaystyle y=mx+b$
Then I made $\displaystyle f'(x)=3$
$\displaystyle 3x^2=3$
$\displaystyle x^2=1$
To get the value of x.
$\displaystyle x=1$
Now I go back to the given line and plug in:
$\displaystyle y=3(1)+1$
$\displaystyle y=4$
My point is $\displaystyle (1,4)$
I did most of it as I was writing this, I think my light bulb turned on.
$\displaystyle y-y1=m(x-x1)$
$\displaystyle y-4=3(x-1)$
$\displaystyle y=3x+1$
Did I do it right or is there another way of doing this?