Question

Find the gradients of the lines that pass through the point (1,7) and are tangent to the parabola y = (2−x)(1+3x).

Answer 1

$y = (2-x)(1+3x)$
$= 2 + 6x - x - 3x^{2}$
$= 2 + 5x - 3x^{2}$

$\frac{dy}{dx} = m = 5 - 6x$

At x = 1:
$\frac{dy}{dx} = m = 5 - 6 = -1$

$y - 7 = -(x - 1)$
$y = -x + 8$
$\therefore y = 8 - x$

Answer 2

Y=(2-x) (1+3x)
This is vertical. and that should be 4x=1