The Winding river is modeled by r(x)= [tex]x^{3}+ 4 x^{2}+4 x+12[/tex]
As bridges will be built along x-Axis to cross the river.
so,the bridges work as a tangent to river.
r'(x)=[tex]3x^{2}+8 x+4[/tex]
So , r'(x)=0
→[tex]3x^{2}+8 x+4[/tex]=0
→3x²+6 x+ 2 x+4=0
→3 x(x+2)+2(x+2)=0
→(x+2)(3 x+2)=0
x=-2, x= -2/3
As there are two values of x, from where we can draw tangents or bridges to the river.So there are maximum of two bridges that we need to built.
