A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $$3{x^4} - 16{x^3} + 24{x^2} + 37$$ is

If $$\,\,\,\,f\,\,\,\,\left( x \right)$$ is defined as follows, what is the minimum value of $$f\,\left( x \right)$$ for $$x \in \left( {0,2} \right)$$ ? $$$f\left( x \right) = \left\{ {\matrix{ {{{25} \over {8x}}\,\,when\,\,x \le {3 \over 2}} \cr {x + {1 \over x}other\,wise} \cr } } \right.$$$

What is the value of $$\int\limits_0^{2\pi } {{{\left( {x - \pi } \right)}^3}\left( {\sin x} \right)dx} $$

The function $$f\left( {x,y} \right) = 2{x^2} + 2xy - {y^3}$$ has