We have that
An equation of the tangent line to the curve y = x sqrt{x} that is parallel to the line y = 6 + 6x. is
From the question we are told
Find an equation of the tangent line to the curve y = x sqrt{x} that is parallel to the line y = 6 + 6x.
Generally the equation for the Tangent is mathematically given as
[tex]y= 6* x + k[/tex]
Where
[tex]\frac{3}{2}*\sqrt{x}=6\\\\x=16[/tex]
Therefore
The Resultant value of y
[tex]Y=64[/tex]
[tex]Hence\\\\64=96 + c\\\\c=-32[/tex]
Therefore
An equation of the tangent line to the curve y = x sqrt{x} that is parallel to the line y = 6 + 6x. is
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