# Inflection help

1. Dec 28, 2007

Hi, can someone help me guide me on how to find inflections? I am not too sure how to do it in such a problem as the follows:

1. The problem statement, all variables and given/known data
Determine a, b, and c so that the function
f(x) = x^3 + ax^2 + bx + c has critical points at (1,5) and an inflection point at (2,3)

2. Relevant equations

3. The attempt at a solution

I am not too sure how to persue this, for critical points I know the derivative needs to equal zero and then you find the critical points that way, but I dont know what to do for the inflection.
Thank You!

2. Dec 28, 2007

### rocomath

1st derivative - critical points

2nd derivative - inflection points

3. Dec 28, 2007

Yep, thanks I figured it out
a = -9/2
b = 11

But I cant find out what c is;
This is wat I did by the way;

y = x3 + ax2 + bx + c

y' = 3x2 + 2ax + b

y'' = 6x + 2a

Take y' and plug in (1, 5)

5 = 3(1) + 2a(1) + b ==> 2a + b = 2 ............ (1)

Take y'' and plug in (2, 3)

3 = 6(2) + 2a ==> a = -9/2 ............... (2)

Then, plug (2) into (1) to find b

b = 11

4. Dec 28, 2007

### Rainbow Child

The points (1,5), (2,3) are $$(x,y)$$ points not $$(x,y')$$ or $$(x,y'')$$ points!

On critical points $$y'(x_o)=0$$

On inflection points $$y''(x_o)=0$$

5. Dec 28, 2007

Ohh, ok, yes, I fixed it now, I have my answer to be

a = -6
b = 9
c = 1

6. Dec 28, 2007

### Rainbow Child

And that's the correct one!