If f'(x)= tan-¹(x3 - x), at how many points is the tangent line to the graph of y = f(x) parallel to the line y = 2x?

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter58: Achievement Review—section Five
Section: Chapter Questions
Problem 30AR: Determine dimension x to 3 decimal places.
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If f'(x) = tan-¹(x²-x), at how many points is the tangent line to the graph of y = f(x) parallel to
the line y = 2x?
(A) None
(B) One
(C) Two
(D) Three
(E) Infinitely many
Transcribed Image Text:If f'(x) = tan-¹(x²-x), at how many points is the tangent line to the graph of y = f(x) parallel to the line y = 2x? (A) None (B) One (C) Two (D) Three (E) Infinitely many
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I understand up to solving for x, please explain how tan^-1 comes across and becomes tan ^2

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