Suppose f is Differentiable On R and a ≤ f’(x) ≤ b for All x ∈ R where a, b> 0. If f (0) = 0, Then

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Question

Suppose f is differentiable on R and a ≤ f’(x) ≤ b for all x ∈ R where a, b> 0. If f (0) = 0, then

easy

Solution

Correct option is

ax ≤ f (x) ≤ bx

For x > 0. Applying Lagrange’s theorem on [0, x] we have c ∈ (0, x) such that

x > 0, similarly for x < 0 applying lagrange’theorem for [x, 0], we have ax ≤ f(x) ≤ bx.

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