Consider the function f(x) = 2x² – 5x – 12. Find

(a) The derivative of f(x) from first principles;

(b) The rate of change of f(x) at x = 1;

(c) The points at which the line through (1, –15) with slope m cuts the graph of f(x);

(d) The value of m such that the points of intersection found in (c) are coincident;

(e) The equation of the tangent to the graph of f(x) at the point (1, –15).