Final answer:
To find the first and second derivatives of y with respect to x given the parametric equations x and y as functions of t, differentiate each with respect to t, and then use the chain rule for derivatives. The curve is concave upward where the second derivative is positive.
Step-by-step explanation:
To find the derivatives dy/dx and d²y/dx² as functions of t given the parametric equations x=2sin(t) and y=3cos(t), we first differentiate both x and y with respect to t to get dx/dt and dy/dt, respectively. Then, to find dy/dx, we simply divide dy/dt by dx/dt. To find d²y/dx², we differentiate dy/dx with respect to t and divide by dx/dt.
The curve is concave upward when d²y/dx² is positive. We evaluate the sign of d²y/dx² by finding the second derivative and determining the interval(s) for t where it is positive.