Originally Posted by

**mark** hi, my question is: find the equations of the tangents to the curve with equation $\displaystyle y = (x + 1)(5 - x)$ at the points P(-1, 0) and Q(5, 0). prove that these two tangents intersect at the point (2, 18)

the first thing i did was expand the brackets and differentiate with x = -1 (for P). which resulted in:

$\displaystyle -x^2 + 4x + 5$ so then $\displaystyle \frac{dy}{dx} = - 2x + 4$ and usig x = -1 the gradient comes to 6

so the equation is $\displaystyle y - 0 = 6(x + 1) \implies y = 6x + 6$

so for Q i did the same thing. used x = 5 for $\displaystyle -2x + 4$ which gave a gradient of - 6

so the equation is $\displaystyle y - 0 = -6(x - 5) \implies y = -6x + 30$

how would i prove these two tangents intersect at point (2, 18)?

thanks, mark