Let f: R → R be a differentiable function such that f((x+y)/3) = (f(x)+f(y))/3 for all x, y R, and f'(0) = 3. Then the minimum value of the function g(x) = 3 + eˣ f(x), is:

Limit, Continuity and Differentiability: JEE Main 2026 Mathematics question

JEE Main 2026 · 5 Apr, Morning shift · Q19

JEE Main 20265 Apr, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f: \mathbb{R} \to \mathbb{R}

be a differentiable function such that

f\left(\frac{x+y}{3}\right) = \frac{f(x)+f(y)}{3}

for all

x, y \in \mathbb{R}

, and

f'(0) = 3

. Then the minimum value of the function

g(x) = 3 + e^x f(x)

, is: