Behaviors of Implicit Relations (College Board AP® Calculus AB): Exam Questions

A curve goes through the point (4, 0). If the equation of the curve satisfies $\left(x+3y\right)\frac{dy}{dx}=5x-2y$, what is the value of $\frac{d^{2}y}{d{x}^2}$ at the point (4, 0)?

A curve has the equation $2x^2-2y^2-3y=0$. Find the number of critical points on this curve.

If $x+y^2=2x^2$, what is $\frac{d^{2}y}{d{x}^2}?$

Which of the following describes the behaviour of the normal line to the curve $y=\sin \left(xy\right)$ at the point $\left(0,0\right)?$

What is an equation of the horizontal tangent line to the curve $2x^2+3y^3=12xy?$

A curve has the equation $xy+x^3+y=0$, where $x\ne -1$.

Find the number of critical points on the curve.

A curve has the equation $y=x{e}^y$. What is the value of the second derivative of the curve at the origin?

Given that a curve has the equation $\sin x\cos y=\frac{1}{2}$, what is an expression for $\frac{d^{2}y}{d{x}^2}$?

Which of the following is a critical point on the curve $x^3+y^3=3xy?$

What can be said is true about the point $\left(-1,-1\right)$ on the curve $x^2+y^2-2xy-4y=4?$