## Related questions with answers

Question

**Find $dy/dx$ and $d^2y/dx^2$, and find the slope and concavity (if possible) at the given value of the parameter.**

$\underline{Parametric\ Equation}$

$x=\sqrt t,\ y=3t-1$

$\underline{Point}$

$t=1$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 6Given:

$\begin{aligned} x&=\sqrt{t} \\ y&=3t-1 \end{aligned}$

We need to determine the derivatives $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$, while also determining the slope and concavity at $t=1$.

The following formula can be used to determine the derivative $\frac{dy}{dx}$ of parametric equations:

$\begin{aligned} \frac{dy}{dx}&=\frac{dy/dt}{dx/dt} \end{aligned}$

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