Question

Write an equation for the tangent line to the curve xy=36 at the point (9,4)

Answer 1

Step 1: Find dy/dx

If xy = 36, then y = 36/x or y = 36 x^(-1).

dy/dx = -36/x^2

Step 2: evaluate dy/dx at (9,4).

dy/dx at (9,4) = -36/(9^2) = -4/9

Step 3: put together your equation in point-slope form:

y - 4 = -4/9(x-9)

or put that into slope-intercept form:

y = -4/9x +8