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

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

Find the points of local maxima and minima if any of the following function defined in $$0 \le x \le 6,$$ $$\,\,\,\,f\left( x \right) = {x^3} - 6{x^2} + 9x + 15.$$