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.