FInd the equation of the tangent line to the curve

Question

Find an equation of the tangent line to the curve
y = x(square root x)
that is parallel to the line
y = 3 + 9x.

Answer 1

 

9 =  y' = x * (1/2)*x^(-1/2)  + sqrt(x)

 

 

9 * sqrt(x) = (1/2)x + x

 

9 * sqrt(x) = (3/2)x

 

6 * sqrt(x) = x

 

36*x = x^2

 

x^2 - 36x = 0

 

x(x-36) = 

 

x=0 or x=36

 

x=0 however is not in the domain of the derivative

 

x=36

 

So the tangent line is parallel at x=36

 

f(36) = 36*6 = 216

 

(36,216) and has slope 9

 

B = y - mx

   = 216 - (9)(36)

   = 216 - 324

   = -108

 

y = 9x - 108