Answer
$(a, 0)$
Work Step by Step
$f'(x) = 3x^2 − 6ax + 3a^2$. By the quadratic formula, this is zero when $$x = \frac{{6a \pm \sqrt {36{a^2} - 36{a^2}} }}{6} = a$$, So the point $(a, 0)$ is a critical point.
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 4 - Applications of the Derivative - 4.1 Maxima and Minima - 4.1 Exercises - Page 244: 66
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