Let f(x) = ax 2 + bx + c be an arbitrary quadratic function and choose two

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Let f(x) = ax2 + bx + c be an arbitrary quadratic function and choose two points x = p and x = q. Let L1 be the line tangent to the graph of f at the point (p, f(p)) and let L2 be the line tangent to the graph at the point (q, f (q)). Let x = s be the vertical line through the intersection point of L1 and L2. Finally, let R1 be the region bounded by y = f(x), L1, and the vertical line x = s, and let R2 be the region bounded by y = f(x), L2, and the vertical line x = s. Prove that the area of R1 equals the area of R2.

L2 y = ax? + bx + c L1 (q.f(q)) (p.f(p)) R2 R1

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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