Graph the function $y=\frac{35}{x^2+5}($Agnesi$\text{'}$s witch$)$ by identifying the domain and any symmetries, finding the derivatives $y^{\text{'}}$ and $y^{\text{'}\text{'}},$ finding the critical points and identifying the function's behavior at each one, finding where the curve is increasing and where it is decreasing, finding the points of inflection, determining the concavity of the curve, identifying any asymptotes, and plotting any key points such as intercepts, critical points, and inflection points. Then find coordinates of absolute extreme points, if any.

Find the domain of the function.

The domain is

$($Type your answer in interval notation.$)$

Identify any symmetries. Choose the correct answer below.

A$.$ The function is an even function that is symmetric about the origin.

B$.$ The function is an even function that is symmetric about the $y-$axis.

C$.$ The function is an odd function that is symmetr$$ about the origin.

D$.$ The function is an odd function that is symmetric about the $y-$axis.

E$.$ The function is neither even nor odd.

Find the derivative $y^{\text{'}}.$

$y^{\text{'}}=$

$$

Find the second derivative $y^{\text{'}\text{'}}.$

$y^{\text{'}\text{'}}=$

$$

Identify any critical points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The critical point$($s$)$ occur$($s$)$ at $x=$

$($Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.$)$

$(1)$ Time Remaining: $01$:$31$:$48$