Let f : 0 , 2 → R be a twice differentiable function such that f ' ' x > 0 , for all x ∈ 0 , 2 . If ϕ x = f x + f 2 – x , then ϕ is

Question

Let f : 0 , 2 &#8594; R be a twice differentiable function such that f ' ' x &#62; 0 , for all x &#8712; 0 , 2 . If &#981; x = f x + f 2 &#8211; x , then &#981; is

Quantrex Academy · Accepted Answer

Correct answer: D. decreasing on 0,1 and increasing on ( 1,2 )

f x : 0,2 &#8594; R and f ' ' x &#62; &#160; 0 &#160; for x &#8712; &#160; [ 0,2 ] &#8658; f ' ( x ) is increasing for x &#8712; &#160; [ 0,2 ] Now, &#981; ( x ) = f ( x ) + f ( 2 - x ) &#8658; &#981; ' x = f ' x - f ' ( 2 - x ) For &#160; x &#8712; &#160; [ 0,1 ) , x &#160; &#60; &#160; 2 &#160; &#8211; &#160; x &#8658; f ' ( x ) &#60; f ' ( 2 - x ) &#8658; &#981; ' ( x ) &#60; 0 For x &#8712; &#160; ( 1 , &#160; 2 ] , x &#160; &#62; &#160; 2 &#160; &#8211; &#160; x &#8658; f &#

Let f : 0 , 2 → R be a twice differentiable function such that f ' ' x > 0 , for all x ∈ 0 , 2 . If ϕ x = f x + f 2 – x , then ϕ is

Options

Correct answer

Step-by-step solution

More from Application of Derivatives

Let f : 0 , 2 &#8594; R be a twice differentiable function such that f &#39; &#39; x &#62; 0 , for all x &#8712; 0 , 2 . If &#981; x = f x + f 2 &#8211; x , then &#981; is

Options

Correct answer

Step-by-step solution

More from Application of Derivatives

Let f : 0 , 2 → R be a twice differentiable function such that f ' ' x > 0 , for all x ∈ 0 , 2 . If ϕ x = f x + f 2 – x , then ϕ is