$\begingroup$Find the equation of a line tangent to $y=3x^2-4x$ and parallel to the line $2x-y+3=0$ number $3$ on the picture ()
$\endgroup$11 Answer
$\begingroup$we have $$y'(x)=6x-4$$ and since the Tangent line is parallel to $$y=2x+3$$ we get $$y'(x)=6x-4=2$$ thus $$x=1$$ for $$x=1$$ we get $$y=-1$$ and our Tangent line has the equation $$y=2x-3$$
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