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

Question

please help

Answer 1

If you want the equation of a line tangent to the curve y = x² , first use power rule to find the derivative:

y' = 2x This will tell you the slope with respect to x.

The given linear equation : y = 6 + 9x, has a slope of 9.

So, to find where the curve y = x² has a slope of 9, solve 2x = 9. This will occur when x = 4.5

On the curve y = x², when x = 4.5, y = 20.25.

So, write the equation of the line in point slope form using m = 9, x₁ = 4.5 and y₁ = 20.25

y = 9(x - 4.5) + 20.25

You may distribute and combine like terms if you prefer it in slope intercept form.