In Quadrant IV, x is positive and y is negative.
The curve defined by x^2/16 - y^2/9 = 1 is a hyperbola. The derivative dy/dx gives the slope of the tangent line to the hyperbola at any point.
In Quadrant IV, x is positive and y is negative, so both dy/dx and 9x/16y are negative. Therefore, the slope of the tangent line to the curve is negative in Quadrant IV.
The second derivative d^2y/dx^2 gives the concavity of the curve. In Quadrant IV, y is decreasing and d^2y/dx^2 is negative, so the curve is concave down in Quadrant IV.
Therefore, the curve is decreasing and concave down in Quadrant IV.