The function is .
Apply first derivative with respect to .
Apply second derivative with respect to .
Determine the values of at which
or
does not exist.
Simplify the expression.
\ or
Solve for .
Solve for .
Here the values of is in imaginary, so does not consider it.
The values of are
and
.
Test for concavity in the intervals ,
and
.
Intervals | \Test value | \ \
Sign of | \
Conclusion | \
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\
| \
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Concave downward | \
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\
| \
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Concave upward | \
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\
| \
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Concave downward | \
\
The function is concave downward in the intervals and
.
The function is concave upward in the interval .