Let , . Answer the…

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

g(x)=\dfrac{e^{x}}{1+e^{x}}

,

x\in\mathbb R

. Answer the following: (i) Find

g'(x)

. (ii) Show that

g'(x)>0

for all

x\in\mathbb R

. (iii) What conclusion can you draw about the existence of local extrema of

g

on

\mathbb R

? Give reasons. (iv) Evaluate

\displaystyle \lim_{x\to -\infty}g(x)

and

\displaystyle \lim_{x\to \infty}g(x)

. Using these limits together with your result from part (ii), comment on the range of

g

.

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