Find the point on the graph of y = x^2 where the tangent line is parallel to the line -3x + 5y = 4

Question

The point on y = x^2 at which the tangent line is parallel to the line −3x + 5y = 4 is ______

Answer 1

y = x²

For a parallel tangent line to -3x+5y = 4, the slope must equal the derivative of the curve.

Putting the line into slope intercept form,

y = 3x/5 + 4/5

The slope, m = 3/5

y' = 2x

2x = 3/5 -->x = 3/10

The point is (3/10, 9/100)