Question

Sketch the graphs of the following functions:

(i) y = 1/(1 + e^-x)

(ii) y = (x³/24) - log x

Answer 1

(i) y = 1/(1 + e^-x)

f'(x) = 0 ⇒ e = 0 which is not possible hence there is no extremum. 

• No vertical asymptote for the curve and the horizontal asymptotes are y = 1 and y = 0

(ii) y = (x³/24) - log x

• The curve exists only for positive values of (x > 0)

(i.e.,) domain is

• No point of inflection 

• No horizontal asymptote is possible 

But the vertical asymptote is x = 0 (y axis)