Find the exact maximum or minimum value of f, and compare it with your answer to part (a).

Question

So part a is it is a maximum and f(x) =1.18

this is the equation

1+x- sqrt(2)(x^2)

could really use help on paring it to a... don't understand it. Thanks!

Answer 1

1+x-√2*x² = f(x)

in a parabola, the vertex is found directly between the zeros of the function.

To find the zeros, we'll use the quadratic formula:

x = [-1 ± √(1 + 4*√2*1)] / 2*-√2

x = (-1 ± 2.58) / -2.83

x = 1.265, -0.558

average of the two zeros: (1.265 - 0.558)/2 = 0.353

So the maximum is located at x = 0.353

the y-value at that point can be found by plugging in 0.353 for x.

1+x-√2*x² = f(x)

1 + 0.353 - √2*(0.353)²

1.353 - 0.177 = 1.176 ≈ 1.18

This matches with part a.