Use the graph to determine

$(c)$ the intervals over which the function is increasing, decreasing, and constant.

For the formula in the following Exercise, is y directly proportional to x ? If so, give the constant of proportionality.

y=9 x-5 x

Determine the intervals over which the function is increasing, decreasing, or constant.

$$f(x)=\sqrt{x^2-1}$$

For this exercise, how does the constant difference in the new column relate to the patterns you observed?

An exponential growth model is appropriate when consecutive function values appear to be changing by a constant

What mathematical constant does $\lim _ { x \rightarrow 0 } ( 1 + x ) ^ { 1 / x }$ appear to equal?

At constant pressure, what role does the enthalpy change play in determining the spontaneity of an event?

When an ideal gas expands at a constant temperature, $\Delta E=0$ for the change. Why?

A population grows exponentially with a proportionality constant of $1.5%.% How long will it take the population to double?

Use the precise definition of a limit to prove that $\lim_{(x,y)\to (a,b)}c=c$ where $c$ is a constant.

Describe how air pressure changes with an increase in altitude. Does it change at a constant rate?

Give the constant term, $a_0$.

$$15-11 t^9-8 t^4$$

Explain why the function f and f+C, where C is a constant, have the same derivative properties.

Determine the derivatives for the given function. Assume $k$ is a constant.

$$P(t)=e^{2 t}$$