Question

Consider the curve in the xy-plane defined by (x^2) − ((y^2) / (5))=1. It is known that dy/dx=(5x)/y and d^2y/dx^2= −25/(y^3). What is true about the curve in Quadrant IV?



Is it concave up or down and why?

Answer 1

well, first off you know that this is an ellipse with center at (0,0), which makes it concave up everywhere below the x-axis.
Since y" > 0 when y < 0, the same holds true.