$\"\"$

The statement is false.

Since the interval of concavity is determined by the $\"\"$ .

Concavity test:

(a) If $\"\"$ for all $\"\"$ in $\"\"$ , then the graph of $\"\"$ is concave upward on $\"\"$ .

(b) If $\"\"$ for all $\"\"$ in $\"\"$ , then the graph of $\"\"$ is concave downward on $\"\"$ .

$\"\"$

Consider an function $\"\"$ .

Apply first derivative on each side with respect to $\"\"$ .

$\"\"$

Apply second derivative on each side with respect to $\"\"$ .

$\"\"$

Determine the values of $\"\"$ at which $\"\"$ or $\"\"$ does not exist.

$\"\"$

The function has inflection point at $\"\"$ .

$\"\"$

Test for concavity in the intervals $\"\"$ and $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Find $\"\"$ at $\"\"$ .

$\"\"$

In the above function $\"\"$ , but $\"\"$ is concave downwards at $\"\"$ .

$\"\"$

The statement is false.