Let R denote the set of all real numbers. Let f : R → R be defined by f ( x ) = { 2 x + s i n x 6 x + s i n x 3 7 if x  = 0 if x = 0 Then which of the following statements is (are) TRUE?

Question

Let R denote the set of all real numbers. Let f : R → R be defined by f ( x ) = { 2 x + s i n x 6 x + s i n x ​ 3 7 ​ ​ if x  = 0 if x = 0 ​ Then which of the following statements is (are) TRUE?

TestHub · Accepted Answer

since 3 > 3 7 ​ ⇒ 3 > f ( 0 ) ⇒ x = 0 is local minima ....option (B) is correct Now, ​ f ( x ) = 2 x + sin x 6 x + sin x ​ = 1 + 2 x + sin x 4 x ​ f ′ ( x ) = ( 2 x + sin x ) 2 4 [( 2 x + sin x ) ⋅ 1 − x ( 2 + cos x )] ​ = ( 2 x + sin x ) 2 4 ( sin x − x cos x ) ​ = ( 2 x + sin x ) 2 4 cos x ( tan x − x ) ​ ​ Options (C) \& (D) are also correct.

Mathematics - Application of Derivative Question with Solution | TestHub

Options:(select one or more)

Doubts & Discussion