If the function f ( x ) = ( 4 − x 2 − 3 ) 2 + ( 4 − x 2 + 1 ) 3 then which of the following is/are correct? ([ . ] denotes GIF)

Question

If the function f ( x ) = ( 4 − x 2 ​ − 3 ) 2 + ( 4 − x 2 ​ + 1 ) 3 then which of the following is/are correct? ([ . ] denotes GIF)

TestHub · Accepted Answer

x ∈ [ − 2 , 2 ] ⇒ a ∈ [ 0 , 2 ] where a = 4 − x 2 ​ f ( a ) = ( a − 3 ) 2 + ( a + 1 ) 3 f ′ ( a ) = 3 a 2 + 8 a − 3 = ( 3 a − 1 ) ( a + 3 ) ∴ f min ​ = f ( a = 3 1 ​ ) = 9 64 ​ + 27 64 ​ = 27 256 ​ ; ∴ f max ​ = f ( a = 2 ) = 28

Mathematics - Application of Derivative Question with Solution | TestHub

Options:(select one or more)

Doubts & Discussion

JEE Advanced (2028)