Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 252: 46

Answer

a. See Graph Below Maximum value is 1.177 b. 1.177; it is the same from part a

Work Step by Step

$f(x)= -\sqrt 2 x^{2}+ x + 1$ a. See Graph Below According to the graph the maximum point of the function is at (0.354, 1.177) Thus the maximum value is 1.177 b. $f(x)= -\sqrt 2 x^{2}+ x + 1$ $f(x) = -\sqrt 2 ( x^2 - \frac {x}{\sqrt 2} + \frac{1}{2\sqrt 2}^2) + 1 + (\frac{1}{2\sqrt 2}^2)(\sqrt 2)$ $f(x) = -\sqrt 2 (x-\frac{1}{2\sqrt 2})^2 + \frac{\sqrt 2 + 8}{8}$ Thus the maximum point of the function is at (0.3536, 1.177), which is equivalent to that of part a.
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