Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Suppose f ′ (x) exists for each x and h(x) = f(x) – (f (x)) 2 + (f (x)) 3 for every real number x. Then:
Text Solution
Verified by ExpertsThe correct answer is:
A
(a and c)
We have
h ′ (x) = f ′ (x) –2f ′ (x) f(x) + 3f ′ (x) f(x) 2
= 3f ′ (x) 
= 3f ′ (x) [(f(x) –1/3) 2 + 2/9]
Thus, h ′ (x) > 0 if f ′ (x) > 0
and h ′ (x) < 0 if f ′ (x) < 0
Therefore, h increases (decreases) whenever f increases
(decreases)
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