The function f(x) = 1 - e^ - x^2 /2 is - Vidyadip

MCQ

The function $f(x) = 1 - {e^{ - {x^2}/2}}$ is

A
Decreasing for all $ x$
B
Increasing for all $ x$
✓
Decreasing for $x < 0$ and increasing for $x > 0$
D
Increasing for $x < 0$ and decreasing for $x > 0$

✓

Answer

Correct option: C.

Decreasing for $x < 0$ and increasing for $x > 0$

c
(c) $f(x) = 1 - {e^{ - {x^2}/2}}$

$f'(x) = - {e^{ - {x^2}/2}}( - x) = x{e^{ - {x^2}/2}}$

For $f(x)$ to be increasing, $f'(x) > 0$

==> $x{e^{ - {x^2}/2}} > 0$

==> $x > 0$ and $f(x)$ to be decreasing for $x < 0$.

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