Evaluate the following derivative using the graph given below.

$\frac{\text{d}}{\text{dx}}{(8f\left(x\right)+12g\left(x\right))}_{x=2}$

Evaluate the following derivative using the graph given below.

${\left(f^{-1}\right)}^{\prime }\left(4\right)$

Identify the function $g$ and value of $a$ such that the following limit represents $g^{\prime }\left(a\right)$. Then, evaluate the limit by finding the value of $g^{\prime }\left(a\right)$.

$\underset{x\to 2}{\lim }\frac{2x^3-16}{x-2}$

A small town's expansion is modeled by the function $S\left(t\right)=-\frac{1}{40}{t}^2+3t+15$, for $0 ≤ t ≤ 60$, where $S$ represents the area in square kilometers and $t$ is the number of years since $2000$. If the population density remains steady at $800$ people per square kilometer, what is the population growth rate in $2025$?

For the function $h\left(x\right)=5\sqrt{x}-3x$, identify all the points on the graph of $h$ where where the graph has a horizontal tangent.

A car accelerates from rest along a straight road and its distance from the starting point is given by the equation $S=\frac{5}{4}{t}^2$, where $S$ is the distance in meters and $t$ is the time in seconds. If the car needs to reach a speed of $90\text{ km/h}$ to safely merge onto a highway, how long will it take to reach this speed, and what distance will the car cover?