Question

Determine where Q(t)=1/2t-ln(1+t^2) is not changing.

Answer 1

differentiate and let the derivative = 0 and solve for t

\[dy/dx = 1/2 - 2t/(1+t^2)\]

so (1 + t^2) = -4t

or

t^2 +4t + 1=0

Use the general quadratic formula to solve

\[t = (-4 \pm \sqrt{4^2 - 4 \times1 \times 1})/(2\times1)\]

Its not changing when
\[t = -2 \pm \sqrt{3}\]

Answer 2

ooh, i didn't expect that the process will be like this. .

Answer 3

Wow thanks, now let me get to it until i can understand.