Consider the function whose first derivative is for all real

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider the function

h

whose first derivative is

h'(x)=x\,e^{-x^{2}}

for all real

x

. At which

x

–value(s) does the graph of

h

have a point of inflection? (a)

x=0

only (b)

x=\pm 1

(c)

x=\pm\dfrac{1}{\sqrt{2}}

(d) The graph of

h

has no points of inflection.