# Thread: Analyze the function for local extreme points, concavity and inflection points

1. ## Analyze the function for local extreme points, concavity and inflection points

$f(x) = 2x^2+2x+3$

Ok, so I know the function is increasing because $f^1(x)=4x+2$ which is positive
also it is concave up because $f^{11}=4$ which is also positive

Please teach me how to solve for local extreme points and inflection points, and for concavity, do I just answer concave up?

2. Originally Posted by jkami
$f(x) = 2x^2+2x+3$

Ok, so I know the function is increasing because $f^1(x)=4x+2$ which is positive Mr F wonders: Is it positive for all values of x ....?

also it is concave up because $f^{11}=4$ which is also positive Mr F says: What is the definition given for concave up in your class notes?

Please teach me how to solve for local extreme points Mr F says: What do your class notes tell you to do?

and inflection points, and for concavity, do I just answer concave up?
..

3. Derivative
If postive, then function increasing
If negative, then function decreasing
If zero, then critical point

Second Derivative
If positive, then concave up
If negative, then concave down
If zero, then inflection point

So I figured the minimum point is $(- \frac 1{2}, \frac 5{2})$, so what is the inflection point

4. Originally Posted by jkami
Derivative
If postive, then function increasing
If negative, then function decreasing
If zero, then critical point

Second Derivative
If positive, then concave up
If negative, then concave down
If zero, then inflection point

So I figured the minimum point is $(- \frac 1{2}, \frac 5{2})$, so what is the inflection point
OK. So where exactly are you stuck in the questions you posted?

5. The problem asked for 3 things

1. extreme points
2. concavity
3. inflection points

I figured

1. extreme point = $(-\frac1{2},\frac5{2})$ at minimum

2. concavity = concave up

Now I still need the inflection point

I noticed that $f^{11}(x) = 4$, so does it mean there are no inflection points?

6. Originally Posted by jkami
[snip]
Now I still need the inflection point

I noticed that $f^{11}(x) = 4$, so does it mean there are no inflection points?
Yes, that's what it means.