4 ms·
Even easier: f(x) = - arctan(x). We have f'(x) = -1/(1+x^2) < 0 for all x, and f''(x) = 2*x/((1+x^2)^2) which has the same sign as x.
by jackmaney 13y ago
Even easier: f(x) = - arctan(x). We have f'(x) = -1/(1+x^2) < 0 for all x, and f''(x) = 2*x/((1+x^2)^2) which has the same sign as x.