Question
Find $d y / d x$ and $d^{2} y / d x^{2}$. For which values of $t$ is the curve concave upward?$$x=t^{2}+1, \quad y=e^{t}-1$$
Step 1
To do this, we first find $dx/dt$ and $dy/dt$. We have $x = t^2 + 1$, so $dx/dt = 2t$. We also have $y = e^t - 1$, so $dy/dt = e^t$. Show more…
Show all steps
Your feedback will help us improve your experience
Carson Merrill and 65 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find $d y / d x$ and $d^{2} y / d x^{2} .$ For which values of $t$ is the curve concave upward? $$x=t^{2}+1, \quad y=t^{2}+t$$
PARAMETRIC EQUATIONS AND POLAR COORDINATES
Calculus with Parametric Curves
Find $d y / d x$ and $d^{2} y / d x^{2}$. For which values of $t$ is the parametric curve concave upward? $$x=t^{3}-12 t, \quad^{2}-1$$
Applications of Differentiation
Derivatives and the Shapes of Curves
Find $d y / d x$ and $d^{2} y / d x^{2} .$ For which values of $t$ is the curve concave upward? $$x=t^{3}+1, \quad y=t^{2}-t$$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD