## anonymous one year ago Calculus 1 Is my shown work correct? Find an equation of the line that is tangent to the graph of f and parallel to the given line. I'll post the equations and my work so far done in the comments

1. anonymous

Find an equation of the line that is tangent to the graph of f and parallel to the given line. $f(x) =x^{3}+2$ and $3x - y + 1 = 0$ This is my solution. Is it correct? $f^{'}= 3x^2$ given line y =3x + 1 m=3 To find where the 2 slopes are equal set f’ prime = m $3x^{2}= 3$ both sides divided by 3 $x^{2}=1$ square root of both sides $x^{2}=\pm1$ Since 1 is a value for x and y = f(x) To determine y, 1 can be plugged into f(x) = $(1)^{3}+2 = 5$ So we have the coordinates (1,5) as well as m = 3. I used $y_{2}-y _{1}= m(x _{2}-x _{1})$ y - 5 = 3(x -1) y - 5 = 3x -3 y = 3x +4

2. jim_thompson5910

y = 3x+4 is one of the solutions there is another tangent line

3. jim_thompson5910

your work looks good so far though