critical points

The function f(x) = 8log e x $$-$$ x 2 + 3 attains its minimum over the interval [1, e] at x = __________. (Here log e x is the natural logarithm of x.)

As $$x$$ varies from $$- 1$$ to $$3,$$ which of the following describes the behavior of the function $$f\left( x \right) = {x^3} - 3{x^2} + 1?$$

Which one of the following graphs describes the function? $$f\left( x \right) = {e^{ - x}}\left( {{x^2} + x + 1} \right)\,?$$

The function $$y = {x^2} + {{250} \over x}$$ at $$x=5$$ attains