Let f ( x ) = x 3 + x 3 1 , x  = 0 . If the intervals in which f ( x ) increases are ( − ∞ , a ] and [ b , ∞ ) then min ( b − a ) is equal to

Question

Let f ( x ) = x 3 + x 3 1 ​ , x  = 0 . If the intervals in which f ( x ) increases are ( − ∞ , a ] and [ b , ∞ ) then min ( b − a ) is equal to

TestHub · Accepted Answer

Here f ′ ( x ) = 3 x 2 − x 4 3 ​ ≥ 0 ⇒ x 6 − 1 ≥ 0 ⇒ x ∈ ( − ∞ , − 1 ] ∪ [ 1 , ∞ ) . ∴ min ( b − a ) = min ( b ) − max ( a ) = 1 − ( − 1 ) = 2 .

Mathematics - Application of Derivative Question with Solution | TestHub