Can someone answer part B?

Question

A quadratic equation is given.

f(x) =1+x−2 x2

(just the two is under the square root)

(a) Use a graphing device to find the maximum or minimum value of the quadratic function f, correct to two decimal places.

f(x)= 1.18

Is this is a maximum or minimum value?

maximum

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

f(x)=

I found the x value for the maximum point being 0.3535533906 using x=-(b/2a). Then I plugged it back into the equation to find the y value to get my answer for the maximum.

My answer was 1.176776695, but according to my online homework, it's not correct.

Answer 1

For f(x) = 1 + x - √2x², you got the correct approximation, at x ≈ 0.3535533906, f(x) ≈ 1.176776695 but, despite being a lot of decimal places this is an approximate value. To find the EXACT value, keep the square root.

x = -b/(2a) = -1/(2(-√2)) = 1/(2√2) = √2/4 and, plugging this into the function gives:

f(√2/4) = 1 + (√2/4) - √2(√2/4)² = 1 + √2/4 - √2(2/16) = 8/8 + 2√2/8 - √2/8 = (8 + √2)/8