A manufacturing company produces $x$ articles per day. The profit function, $P\left(x\right)$, can be modelled by the function $P\left(x\right)=2x^3-81x^2+840x$. Find the range of values of $x$ for which the profit is decreasing.

Find the coordinates of the stationary points on the following curve and determine the nature of the stationary point. Sketch the graph of the function and use graphing software to check your graph.

$y=x^2-4x+8$.

Find the coordinates of the stationary points on the following curve and determine the nature of the stationary point. Sketch the graph of the function and use graphing software to check your graph.

$y=(3+x)(2-x)$.

Find the coordinates of the stationary points on the following curve and determine the nature of the stationary point. Sketch the graph of the function and use graphing software to check your graph.

$y=x^3-12x+6$.

Find the coordinates of the stationary points on the following curve and determine the nature of the stationary point. Sketch the graph of the function and use graphing software to check your graph.

$y=10+9x-3x^2-x^3$.

Find the coordinates of the stationary points on the following curve and determine the nature of the stationary point. Sketch the graph of the function and use graphing software to check your graph.

$y=x^4+4x-1$.

Find the coordinates of the stationary points on the following curve and determine the nature of the stationary point. Sketch the graph of the function and use graphing software to check your graph.

$y=(2x-3{)}^3-6x$.

Find the coordinates of the stationary points on the following curve and determine the nature of each stationary point.

$y=\sqrt{x}+\frac{9}{\sqrt{x}}$.

Find the coordinates of the stationary points on the following curve and determine the nature of each stationary point.

$y=4x^2+\frac{8}{x}$.