Problem $2$: Pollutant Dispersion Analysis

The concentration of a pollutant in a river is given by $C(x)=3x^2-5x+4,$ where $C(x)$ is the concentration in $m\frac{g}{L},$ and x is the distance from the pollution source in kilometers.

Compute the first derivative $C^{\text{'}}(x)$ at $x=2$ using forward, backward, and central difference methods with $h=0\mathrm{.}1.$

Compute the second derivative $C^{\text{'}\text{'}}(x)$ at $x=2$ using the same methods.

Discuss how $C^{\text{'}}(x)$ and $C^{\text{'}\text{'}}(x)$ relate to the rate of change and curvature of pollutant dispersion in the river.