Question

If ƒ(x) = dt, find the interval in which ƒ(x) is increasing –

• A. (0, )
• B. (–, 0)
• C. (–2, 2)
• D. No where

Answer 1

Answer: (B)

(–, 0)

Answer 2

ƒ(x) = dt

\ Ģ(x) = 2x $\left[ \mathrm { e } ^ { - \left( \mathrm { x } ^ { 2 } + 1 \right) ^ { 2 } } - \mathrm { e } ^ { - \left( \mathrm { x } ^ { 2 } \right) ^ { 2 } } \right]$

= 2x $\mathrm { e } ^ { - \left( \mathrm { x } ^ { 4 } + 1 + 2 \mathrm { x } ^ { 2 } \right) } \left[ 1 - \mathrm { e } ^ { 2 \mathrm { x } ^ { 2 } + 1 } \right]$ .

Now ƒ¢(x) > 0 for x Ī (– , 0).