$\"\"$

Probability density function is given by $\"\"$ .

Find second derivative of the probability density function with respect to $\"\"$ .

Consider $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

Find the inflection points by equating the $\"\"$ .

$\"\"$

Exponential function can never be zero.

$\"\"$

Therefore, probability density function has inflection points at $\"\"$ .

$\"\"$

Probability density function has inflection points at $\"\"$ .