Question

The function y = x − x 3 has
(A) no inflection point (B) one inflection point
(C) two inflection points (D) three inflection points

Answer 1

y=x-x^3

So dy/dx = 1-3x² and d²y/dx²= -6x

To find inflection points; dy/dx = 0 and d²y/dx² = 0

⇒ 1-3x² = 0 and -6x=0

⇒ x=√(1/3) or -√(1/3)  and x=0

⇒No value of x satisfies both the conditions

So there is no inflection point (option A)