In the context of derivatives as functions, what does the derivative of a function represent?

Temperature The given graph shows the outside temperature T in °F, between 6 a.m. and 6 p.m.

b. At what time does the temperature increase most rapidly? Decrease most rapidly? What is the rate for each of those times?

For the function $f\left(x\right)=3x^2$, what is the multiplicative rate of change of the function, that is, what is its derivative as a function of $x$?

Suppose the graph of the function $f\left(x\right)$ passes through the points $(2,3)$ and $(4,7)$. What is the average rate of change of $f\left(x\right)$ between $x=2$ and $x=4$? Round your answer to the nearest tenth.

Given the function $f\left(x\right)=x^2$, which of the following is the average rate of change of $f\left(x\right)$ on the interval from $x=3$ to $x=6$?

The slope of the tangent line at a point on a function calculates which of the following?

Which of the following best describes the derivative of a function $f\left(x\right)$?

Consider the function $f\left(x\right)$ whose second derivative is $f^{″}\left(x\right)=6x$. If $f\left(0\right)=2$ and $f^{\prime }\left(0\right)=3$, what is $f\left(x\right)$?

For the function $f\left(x\right)$, in which direction(s) does the derivative $f^{\prime }\left(x\right)$ provide information about the behavior of $f\left(x\right)$?