Originally Posted by

**mark** hi, my question is: the equation of a curve is $\displaystyle y = (x - 8)(x - 2)$ find the gradient of the curve

a) at the point where the curve crosses the y-axis,

b) at each of the points where the curve crosses the x-axis

for a) i expanded the brackets then differentiated:

$\displaystyle x^2 - 2x - 8x + 16 \implies x^2 - 10x + 16 \implies \frac{dy}{dx} = 2x - 10$ since x is zero on the y-axis the answer must be -10 and my book confirms this.

for b) i just made it $\displaystyle 2x - 10 = 0 \implies 2x = 10 \implies x = 5$ but i don't think this is going in the right direction as the answer the book gives is "6 and -6"

could someone show me how its done please?

thanks, mark