This question: $1$ point$($s$)$ possible

Find the open intervals where the function is concave upward or concave downward. Find any inflection points.

$f(x)=-2x^3+3x^2+167x-5$

Where is the function concave upward and where is it concave downward? Select the correct choice below and, if necessary, fill in the answer box$($es$)$ to complete your choice.

A$.$ The function is concave upward on the interval$($s$)$ and concave downward on the interval$($s$)$

$($Type your answers in interval notation. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed.$)$

B$.$ The function is concave downward on the interval$($s$)$ The function is never concave upward.

$($Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.$)$

C$.$ The function is concave upward on the interval$($s$)$ The function is never concave downward.

$($Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.$)$

D$.$ The function is never concave upward or downward.

Find any inflection points of $f,$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The function has an inflection point at $.$

$($Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed. $)$

B$.$ The function $f$ has no inflection points