The maximum value of f x = x 4 + x + x 2 on [ - 1 ,   1 ] is

Question

The maximum value of f x = x 4 + x + x 2 on [ - 1 , &#160; 1 ] is

Aicharya · Accepted Answer

∵ f x = x 4 + x + x 2 On differentiating w.r.t. x , we get f ′ x = 4 + x + x 2 - x ( 1 + 2 x ) 4 + x + x 2 2 For maximum, put f ′ x = 0 ⇒ 4 - x 2 4 + x + x 2 2 = 0 Given x ∈ [ − 1 , 1 ] ⇒ x 2 ∈ [ 0 , 1 ] ⇒ 4 − x 2 > 0 ⇒ f ′ ( x ) is increasing in [ − 1 , 1 ] and its maximum value will be f ( 1 ) = 1 6 .

The maximum value of f x = x 4 + x + x 2 on [ - 1 , &#160; 1 ] is

Solution

The maximum value of f x = x 4 + x + x 2 on [ - 1 , 1 ] is