9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Second Derivatives Of Parametric Equations — Quiz

Test your understanding of second derivatives of parametric equations with 5 practice questions.

Practice Questions

Question 1

For parametric equations $x=f(t)$ and $y=g(t)$, which formula gives the second derivative of $y$ with respect to $x$?

Question 2

If $x=t^2$ and $y=t^3$, what is $\frac{dy}{dx}$ when $t=2$?

Question 3

If $x=t^2$ and $y=t^3$, what is $\frac{d^2y}{dx^2}$ when $t=2$?

Question 4

If a parametric curve has $\frac{d^2y}{dx^2}>0$ at a point, what does that tell you about the graph of $y$ as a function of $x$ there?

Question 5

If $x=\sin t$ and $y=\cos t$, what is $\frac{dy}{dx}$ when $t=\frac{\pi}{4}$?