Mathematics

Mathematics

Problem

Let

\mathbb{R}

be real numbers and

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

be a differentiable function such that

\forall x, y \in \mathbb{R}, |f(x) - f(y)| \le |x - y|^{2025}

and

f(100) = 1

, then the area bounded by curve

y = \min\{f(x), x^2, e^{2-x}\}

, x-axis and line

x = 4

. In sq. units is

K

. Then which of the following is/are true? (A)

K < \frac{7}{3}

(C)

K > \frac{7}{3}

(B)

K = \frac{7}{3} - \frac{1}{e^2}

(D)

K = \frac{7}{3} + \frac{1}{e^2}

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