Question

find a point on the graph of y=x^2 -3x where the tangent line is parrallel to the line -x+y=11

Answer 1

your line has slope 1, so you want the point tangent line to also have slope 1
take the derivative, set it equal to 1, and solve

Answer 2

\[y'=2x-3\]
\[1=2x-3\]
\[x=2\] and so if x = 2 then
\[y=2^2-3\times 2=-2\]