Local Extrema! urgent



You should be familiar with the exponential function e^x.

Does its graph have any local extrema ?

(Note: Subtracting 2 from x does nothing to alter that shape of the graph; it results only in a horizontal shift.)

Please share what you've thought about, so far, in this exercise.

 
Tamersaideh said:
[Does] it have a local max at infinity No - it grows forever.

Also, there exists no location that we can call "at infinity".

I mean, infinity is not a number; it's only a concept.


and local min at y = 0 No.

When y = e^x, the value of y never equals zero.

e^x is always a positive number.
Click to expand...

e^x approaches infinity, as x grows without bound.

Hence, no matter how big you think e^x has become, you can always make it bigger.

The graph of e^x has no maximum value.

e^x never equals zero, and e^x is always a positive number.

No matter how close to zero you think e^x is, you can always make it smaller.

The graph of e^x has no minimum value.

Once you become familiar with the graph of y = e^x, here are two facts that tell you e^x has no local minimums or local maximums:

The graph of e^x is continually increasing, as x goes from -? towards +?

The graph of e^x is continually decreasing, as x goes from +? towards -?

Next, you need to realize that shifting any graph horizontally does nothing to change its shape.

In other words, the global behavior of e^x is the same as e^(x - 2).

You might need to review precalculus.

 
You must log in or register to reply here.
Top