A differentiable function f is increasing on an interval if its derivative f'(x) is greater than or equal to 0 (strictly increasing if f'(x) > 0) for all x in that interval. It is decreasing if its derivative f'(x) is less than or equal to 0 (strictly decreasing if f'(x) < 0) for all x in that interval. So the sign of the first derivative tells us whether the function rises or falls.

f'(x) > 0 increasing; f'(x) < 0 decreasing

Find the derivative: f'(x) = 2x - 4 = 2(x - 2). Set f'(x) = 0 to get the critical point: x = 2. For x < 2, f'(x) < 0, so the function is decreasing on (-infinity, 2). For x > 2, f'(x) > 0, so the function is increasing on (2, infinity). Thus f is decreasing on (-infinity, 2) and increasing on (2, infinity).

The slope of the tangent to a curve y = f(x) at a point is the value of the derivative dy/dx at that point. The normal is the line perpendicular to the tangent at that point, so its slope is the negative reciprocal of the tangent's slope, that is, slope of normal = -1/(dy/dx). Using the point-slope form with these slopes gives the equations of the tangent and the normal.

slope of normal = -1/(slope of tangent)