1. The problem statement, all variables and given/known data f(x) = 2x2-5x-12 is given; part a: find derivative of f(x) using first principles, part b: find the rate of change of f(x) at x=1, part c: the points at which the line through (1, -15) with slope m cuts the graph of f(x), part d: the value of m such that the points of intersection found in (c) are coincident, part e: the equation of the tangent to the graph of f(x) at the point (1, -15) 2. The attempt at a solution I found the derivative first, using first principles, it is f'(x) = 4x - 5 Then for part b, the rate of change of f(x) at x = 1, it's the f'(x) value at x = 1, which is -1, the slope of tangent. I am stuck at part c. I first got the line equation; y-y1=m(x-x1) using point (1, -15), which gives y = mx-m-15 So to find the intersection points with this line and f(x), I tried to equate them both and solve, mx-m-15 = 2x2-5x-12, and end up at the following, 2x2-(5-m)x+(m+3)=0 how do I solve this? or is my approach wrong? And what is that part d is asking? I didn't understand it. Thanks!