Question

Find an equation of the line that is tangent to the graph of f and parallel to the given line.
Function f(x) = x^2 − x
Line x + 3y − 6 = 0

Answer 1

\[\]\[f(x)=x^2-x\]\[y=(6-x)/3\]\[m=-1/3\]\[f'(x)=2x-1\]\[-1/3=2x-1\]\[2/3=2x\]\[x=1/3\]\[f'(1/3)=-1/3\]\[y=-x/3+b\]\[(1/3,\ f(1/3))=(1/3,\ -2/9)\]\[b=y+x/3\]\[b=-2/9+1/9\]\[b=-1/9\]\[line=-x/3-1/9\]