Published by:
CGP EDU Academic Team
Published on: August 14, 2026
(i)If f(x) = 
+ 
, then prove that f ′ (x) = 0 ∀ x ∈ R.
(ii) Find the value of x for which function f(x) = 
t(e t – 1) (t – 1) (t – 2) 3 (t – 3) 5 dt has a local minimum
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(ii) 1, 3
Sol. (i) f ′ (x) = sin –1 
. 2 sinx cosx – cos –1 
. 2 cosx sinx
= x . sin 2x – x sin 2x = 0
(ii) f(x) = 
; 
= f ′ (x) = x.(e x –1)(x – 1) (x –2) 3 (x –3) 5
change of sign 
Points of minima x = 1, 3 x = 1, 3
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