Using the power rule, [tex]g'(a) = 2x-3[/tex].
At x = 0, [tex]g'(0)=-3[/tex]. Therefore, the slope of the tangent line is -3. In point-slope form, the equation of the line tangent to the curve at (0,3) is [tex]y-3=-3(x-0)[/tex].
At x = 2, [tex]g'(2)=1[/tex]. Therefore, the slope of the tangent line is 1. In point-slope form, the equation of the line tangent to the curve at (2,1) is [tex]y-1=1(x-2)[/tex].
