Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let f (x) = 
(i) Total number of points of inflection in the curve are
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Ans.
(i)
Sol. f(x) = 
f ' (x) = 
= 
f '' (x) = 
= 
f '' (x) = 0 ⇒ x(x – 
) (x + 
) = 0
Clearly x = 0, – 
, 
are points of inflexion
(ii)
Sol. f ' (– 
) = 
= 
, f ' ( 
) = 
,
f '(0) = 1, 
f ' (x) = 0 and 
f ' (x) = 0
∴ greatest slope = 1
(iii)
Sol. Since f (x) is odd function
∴ f iv (x) is an odd function
Which is defined at x = 0
∴ f iv (0) = 0
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