Solve Integration Problem Homework: Jennie

[JenniferBlanco]

Homework Statement

I don't know how to make the integral sign so I am took a picture of the question.

http://img99.imageshack.us/img99/4139/mathquestional7.jpg

Homework Equations

Equations are located in the above img.

The Attempt at a Solution

I first integrated the first derivative and got -

(ax^3)/3 + (bx^2)/2

plugged in 1 and got -

6=a + b

Then I got the second derivative --> 2ax +b and plugged in f''(1) and got: 18 = 2a +b

Using both the equations, I figured out that:
a=12
b=-6

how do I find the contant c to get f(x)?-Jennie

 

[EnumaElish]

how do I find the contant c to get f(x)?

By using (iii)?

I am assuming you meant f(x) = (ax^3)/3 + (bx^2)/2 + c.

 

[JenniferBlanco]

I tried using (iii) and this is what I got -

f(x) = 4x^3 -3x^2 + c

then I plugged in 2 and 1 and got -

(32-12+c) - (4-3+c) = 18

but then c will cancel out.

I am sure I am doing this wrong. please guide me

 

[EnumaElish]

What do you get when you integrate 4x^3 -3x^2 + c without limits?

 

[JenniferBlanco]

x^4 - x^3 + cx

 

[EnumaElish]

Shouldn't it be x^4-x^3+cx?

 

[JenniferBlanco]

yes, i edited it before you replied.

 

[EnumaElish]

What do you get for x=1? For x = 2?

 

[JenniferBlanco]

when x=1 then I got c
when x=2 then I got 8+2c

 

[EnumaElish]

Do you think you can use (iii)?

 

[JenniferBlanco]

Thank you!

so,

(8 +2c) - c = 18
and c = 10

that gives me--> f(x)= 12x^2 - 6x + 10

 

[EnumaElish]

Do you mean f(x) = 4x^3 -3x^2 + 10?

 

[JenniferBlanco]

aaah yes. I was writing it down and was wondering how 6=18.

Sorry for the error and Thanks for the help. :)