Perform a first derivative test on the function $f(x)=2x^2+x+3$;$[-3,3].$

a$.$ Locate the critical points of the given function.

b$.$ Use the first derivative test to locate the local maximum and minimum values.

c$.$ Identify the absolute maximum and minimum values of the function on the given interval $($when they exist$).$

a$.$ Locate the critical points of the given function. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The critical point$($s$)$ is$/$are at $x=$

$($Simplify your answer. Use a comma to separate answers as needed.$)$

B$.$ The function does not have a critical point.

b$.$ Locate the minimum value. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A$.$ There is a local minimum at $x=$

$($Simplify your answer.$)$

B$.$ There is no local minimum.

Locate the maximum value. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A$.$ There is a local maximum at $x=$

$($Simplify your answer.$)$

B$.$ There is no local maximum.

c$.$ Identify the absolute minimum value of the function. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ The absolute minimum value is

$($Simplify your answer.$)$

B$.$ There is no absolute minimum.

Identify the absolute maximum value of the function. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A$.$ The absolute maximum value is

$($Simplify your answer.$)$

B$.$ There is no absolute maximum.