Answer:
See Below.
Step-by-step explanation:
We want to show that the function:

Increases for all values of <em>x</em>.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
![\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5Be%5Ex%20-%20e%5E%7B-x%7D%5Cright%5D)
Differentiate:

Simplify:

Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>
Answer:
180 minutes
Step-by-step explanation:
Starting with the distance formula ...
d = rt
dividing by the coefficient of t will give an equation for t:
t = d/r
Ryan's rate of 4 miles per hour can be expressed in minutes as 4 miles per 60 minutes. The Ryan's time is ...
t = (12 mi)/(4 mi/60 min) = 12·60/4 min = 180 min
Ryan's time is 180 minutes.
Step-by-step explanation:
The right choice is: A <em>whole</em> number constant could have been <em>subtracted</em> from the <em>exponential</em> expression.
Let be an <em>exponential</em> function of the form
, where
and
are <em>real</em> numbers. A <em>horizontal</em> asymptote exists when
, which occurs for
.
For this function, the <em>horizontal</em> asymptote is represented by
and to change the value of the asymptote we must add the <em>parent</em> function by another <em>real</em> number (
), that is to say:
(1)
In this case, we must use
to obtain an horizontal asymptote of -3. Thus, the right choice is: A <em>whole</em> number constant could have been <em>subtracted</em> from the <em>exponential</em> expression.
To learn more on asymptotes, we kindly invite to check this verified question: brainly.com/question/8493280