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find an equation of the tangent line to the curve y=x√x that is parallel to the line y=3+6x

Need help to sold the Calculus problem  find an equation of the tangent line to the curve y=x√x that is parallel to the line y=3+6x

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Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
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Slope of the line y = 6x+3 is 6
 
y = x√x = x3/2
 
   y' = (3/2)x1/2 = slope of tangent line at (x, x3/2)
 
   Since the tangent line is parallel to the line y = 6x + 3, (3/2)x1/2 = 6
 
                                                                                          x1/2 = 4
 
                                                                                              x = 16
 
   Point on tangent line:  (16, 163/2) = (16, 64)
 
   So, the tangent line has slope 6 and passes through the point (16,64).
 
       Equation of tangent line:  y - 64 = 6(x - 16)
 
                                                    y = 6x - 32
                                                

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