Find an equation of the tangent line to the curve y = x x that is parallel to the line y = 9 + 6x.

Answer 1

y = xx = x^2 has slope = 2x = y'

a line parallel to y=9+6x has slope = 6

2x=6

x =6/2 = 3, which is the point (3,9) on the parabola curve

the tangent line is y=6x + b, calculate b by plugging in the point (3,9)

9=6(3) + b

b = 9-18 - -9

y=6x -9 is the equation of the tangent line to y=x^2 parallel to y=9+6x

(this all assumes the problem given as y=xx means y=x times x or x^2, but that's the only interpretation that makes sense. Otherwise, there's a typo in the problem somewhere.)

Answer 2

y = xx = x^2 has slope = 2x = y'

a line parallel to y=9+6x has slope = 6

2x=6

x =6/2 = 3, which is the point (3,9) on the parabola curve

the tangent line is y=6x + b, calculate b by plugging in the point (3,9)

9=6(3) + b

b = 9-18 - -9

y=6x -9 is the equation of the tangent line to y=x^2 parallel to y=9+6x