Question

Determine the inputs that yield the minimum values for each function. Compute the minimum value in each case
F(x) = (4x^2 − 4x + 163)^1/2

Answer 1

Refer to the attachment from Mathematica 9.

Answer 2

f(x)=(4x^2 -4x+163)^1/2
f(x)=(4x^2-4x+1+162)^1/2
f(x)=((2x-1)^2+162)^1/2
if we choose x=1/2 then the minimum of f(x) is (162)^1/2

Answer 3

\[\sqrt{162}=9 \sqrt{2} \]

Answer 4

yes.It means the range of this function is \[f(x)\ge 9\sqrt{2}\]