Let ƒ: [0, 2] → R be a twice differentiable function such that ƒ''(x) > 0, for all x (0, 2). If φ (x) = ƒ(x) + ƒ(2 – x), then φ is:

(B) decreasing on (0, 1) and increasing on (1, 2)

(D) increasing on (0, 1) and decreasing on (1, 2)

Limit, Continuity and Differentiability: JEE Main 2019 Mathematics question

JEE Main 2019 · 8 Apr, Morning shift · Q2710

JEE Main 20198 Apr, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let ƒ : [0, 2]

\to

R be a twice differentiable function such that ƒ''(x) > 0, for all x

\in

(0, 2). If

\phi

(x) = ƒ(x) + ƒ(2 – x), then

\phi

is :