Let ' a ' ( a

Question

Let ' a ' ( a < 0 , a ∈ / I ) be a fixed constant and ' t ' be a parameter then the set of values of ' t ' for the function f ( x ) = ( ∣ [ t ] + 1∣ + 1 − a ∣ [ t ] + 1∣ + a ​ ) x to be a non increasing function of x , ([.] denotes the greatest integer function) is

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f ′ ( x ) ≤ 0 ⇒ ∣ [ t ] + 1∣ + 1 − a ∣ [ t ] + 1∣ + a ​ ≤ 0 , but as a < 0 , 1 − a > 0 . So, ∣ [ t ] + 1∣ ≤ − a ⇒ a ≤ [ t ] + 1 ≤ − a ⇒ a − 1 ≤ [ t ] ≤ − a − 1 ⇒ [ a ] ≤ [ t ] ≤ [ − a ] − 1 ( a s a ∈ / I ) ⇒ [ a ] ≤ t < [ − a ]

Mathematics - Application of Derivative Question with Solution | TestHub

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