Originally Posted by **mr fantastic on an alternative world-line**

Since you know you've gone wrong, you're obviously getting an answer different to the given one. It would be useful to see your working, that is, to see how you got your answer. Did you follow this basic approach:

1. $\displaystyle \frac{dy}{dx} = \frac{3}{2 \sqrt{3x + 11}}$ therefore the gradient of the tangent to the curve at P is given by m = .....

2. A point on the tangent to the curve at P is (3, $\displaystyle \sqrt{20}$), that is, (3, $\displaystyle 2 \sqrt{5}$).

3. The equation of any line (including a tangent) has the general form $\displaystyle y - y_1 = m(x - x_1)$.

4. Conclude that the given answer of $\displaystyle 3x - 4 \sqrt{5} y +$ 31 = 0 is correct.