Let f and g be differentiable on R and suppose f(0) = g(0) …

Maths Differentiation and Applications of Derivatives Maxima and Minima Subjective Type

Published on: August 13, 2026

Let f and g be differentiable on R and suppose f(0) = g(0) and f ′ (x) ≤ g ′ (x) for all x ≥ 0. Then show that f(x) ≤ g(x) for all x ≥ 0.

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The correct answer is:

CHECK THE SOLUTION.

Let h(x) = f(x) – g(x)

h(0) = f(0) – g(0)

⇒ h(0) = 0

h ′ (x) = f ′ (x) – g ′ (x) ≤ 0 for x ≥ 0

⇒ h(x) is decreasing for x ≥ 0 ⇒ x ≥ 0 , h(x)

x ≥ 0

h(x) ≤ h(0)

h(x) ≤ 0

f(x) – g(x) ≤ 0

f(x) ≤ g(x)

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