# Find the polynomial

1. Jun 10, 2013

### utkarshakash

1. The problem statement, all variables and given/known data
Find a polynomial f(x) of degree 4 which increases in the intervals (-∞,1) and (2,3) and decreases in the interval (1,2) and (3,∞) and satisifes the condition f(0)=1

2. Relevant equations

3. The attempt at a solution
Let f(x)=ax^4+bx^3+cx^2+dx+1
f'(1)=f'(2)=f'(3)=0

But using the above results I get only 3 eqns whereas there are 4 variables.

2. Jun 10, 2013

### ehild

You have to find one polynomial from the infinite many which obey the conditions.

ehild

3. Jun 11, 2013

### utkarshakash

I still can't figure out.

4. Jun 11, 2013

### dirk_mec1

There are a lot of polynomials which satisfy the requirements. Luckily you only need ONE of them, get it?

5. Jun 11, 2013

### HallsofIvy

What you are being told is that this problem does NOT have a single, unique, answer. You can use the three equations to solve for three of a, b, c, and d, in terms of the other one. Then just arbitrarily choose a value for that one to get one such polynomial out of the infinite number that satisfy these conditions.

6. Jun 11, 2013

### LCKurtz

That doesn't help us to help you. Nor does it show any effort.

Halls just told you how to work the problem. Have you tried that?