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)`


`(dy)/(dx) = m = 5 - 6x`

At x = 1:

`(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