The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at

Angle between the tangents to the curve $$y = {x^2} - 5x + 6$$ at the points $$(2,0)$$ and $$(3,0)$$ is

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is

Let f be differentiable for all x. If f(1) = -2 and f'(x) $$ \ge $$ 2 for
x $$ \in \left[ {1,6} \right]$$, then