Find the coordinates of the point on h(x) = x^2-x where the tangent line has the equation 3x-9y=4

Answer 1

At the tangent point, h' must equal the slope of the tangent line, so

h'(x) = -3/-9 = 1/3

h'(x) = 2x - 1 = 1/3

x = (1/3 + 1)/2 = 2/3

y = h(2/3) = (2/3)² - 2/3 = -2/9