(i) is already solved for & answers are provided separately.
I'm using a method for differentiation from a text book that should yield root values of -1/2 & 1/2. However, my final solution for slope m yields just 1/2...? Can anyone help me solve for -1/2 using this method? Many thanks.
Q. A line L, with negative slope m, passes through the point (4,2). L interacts the x-axis at a, & the y-axis at b. (Please see attachment) (i) Find the equation of L &, hence, express the coordinates of a & b in terms of m, (ii) Find the value of m, if the area of the triangle aob is a maximum &, hence, find this area.
(i) Equation of L: mx - y - 4m + 2 = 0; a = (, 0), b = (0, -4m + 2)
Attempt: (ii) Area of Triangle: [(y2 - y1)(x1 - x3) - (x2 - x1)(y1 - y3)] => [(0 - 0)( - 0) - (0 - ())(0 - (-4m + 2))] => [0 - ()(4m - 2)] =>  => => =>
= = 0 => 8m = 4 => m =
Ans. (From text book): m = -