Question

If a function f(x) satisfies the condition |f(x) – f(y)| ≤ (x – y)², ∀ x, y ∈ R. Find an equation of tangent to the curve y = f(x) at the point (1, 2).

Answer 1

Given condition is |f(x) – f(y)| ≤ (x – y)²

Thus, y = f(x) = c which is passing through (1, 2).

Thus, c = 2

Hence, the equation of the tangent to the curve at (1, 2) is y = 2.