Let f(x) denote the probability density function of a normal random variable with mean and variance 2. Show that and

Let f(x) denote the probability density function of a normal random variable with mean μ and variance σ2. Show that μ − σ and μ + σ are points of inflection of this function. That is, show that
f″(x) = 0 when x = μ − σ or x = μ + σ.