First slide

Evaluation of definite integrals

Question

Let $f (x) = \int_{1}^{x} e^{- t^{2} / 2} (1 - t^{2}) d t$ then

Moderate

A

$f$ has maximum at $x = 0$
B

$f$ has minimum at $x = - 1$
C

$f$ has maximum at $x = - 1$
D

$f$ has no critical point

Solution

$f^{'} (x) = e^{- x^{2} / 2} (1 - x^{2}) > 0$ for $- 1 < x < 0$ and is negative for $x < - 1 . f (x)$ has minimum at $x = - 1 .$

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