The function f(x)f(x)f(x) is defined by f(x)=∫0xe−t2dtf(x) = \int_{0}^{x} e^{-t^2} dtf(x)=∫0xe−t2dt. Which statement is true regarding f(x)f(x)f(x)?
f′(x)=e−x2f'(x) = e^{-x^2}f′(x)=e−x2
f′(x)=−2xe−x2f'(x) = -2x e^{-x^2}f′(x)=−2xe−x2
f(x)f(x)f(x) has no local extrema.
f(x)f(x)f(x) is periodic.