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

Answer 1

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

If y=x², then the slope of the tangent line to f(x)=x² is (d/dx)f(x)=(d/dx)(x²)=2x

So the equation y=2x gives the slope of the tangent lines to the curve y=x²

Now the line y=9+9x=9x+9=mx+b (the slope-intercept form) says the slope of the line y=9x+9 is 9.

When the slope of the tangent line to y=x² is parallel, that means that line must also have a slope of 9. So at that point, y=2x=9 or x=9/2.

At that point, y=x²=(9/2)²=81/4

So we know the slope, m=9, and we know a point on the line (9/2,81/4)

y=mx+b

81/4=(9)(9/2)+b

b=81/4-81/2=-81/4

y=9x-81/4