Consider the quadratic function f(x) = αx2 + βx + γ. By Lagrange theorem we know that for any a, b ∈ R, with a < b, there is a c ∈ (a, b) such that f(b) − f(a) = f′(c)(b − a). (i) Find c in terms of a and b. (ii) Provide a geometric significance of the result obtained in part (i).

Consider the quadratic function f(x) = αx2 + βx + γ. By Lagrange theorem we know that for any a, b ∈ R, with a < b, there is a c ∈ (a, b) such that f(b) − f(a) = f′(c)(b − a). (i) Find c in terms of a and b. (ii) Provide a geometric significance of the result obtained in part (i).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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Question

Consider the quadratic function f(x) = αx2 + βx + γ. By Lagrange
theorem we know that for any a, b ∈ R, with a < b, there is a c ∈ (a, b)
such that
f(b) − f(a) = f′(c)(b − a).
(i) Find c in terms of a and b.
(ii) Provide a geometric significance of the result obtained in part (i).

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