|
Question 896081: Sketch the graph of a function f(x) that satisfies the stated condition. Mark any inflection points by writing IP on your graph. (I understand there will be more than one answer).
f is continuous and differentiable everywhere.
f(0)=4
that is a zero in the parentheses.
Please help this is the simplest equation right now, there more complex equations in this chapter. Please help.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Fact #1:
"f is continuous and differentiable everywhere."
so f(x) is some smooth curve that has no holes, jumps, or breaks of any kind. You have to keep your pencil down to the paper the entire time when you are drawing this curve. This ensures that the graph is continuous over its entire domain (the set of real numbers)
It's also "differentiable everywhere" which means that there are no sharp cusps or breaks that result in a sharp changes in the slope of the tangent lines. These breaks point to places where you don't have differentiability.
-------------------------------------------------------
Fact #2:
"f(0)=4 "
This means that the point (0,4) is on the graph. Put another way, the curve goes through (0,4). This is the y-intercept
We cannot determine anything about the inflection points based on these two given facts.
-------------------------------------------------------
So all you have to do is draw some continuous curve (continuous everywhere) that is also smooth enough so that it's also differentiable everywhere. This means you don't have any sharp turns or breaks and you don't have any vertical tangent lines. Furthermore, you have to make sure this curve passes through (0,4)
|
|
|
| |
