# Homework Help: Finding unknown constants

1. Apr 19, 2015

### MrJamesta

1. The problem statement, all variables and given/known data
determine the constants a,b,c, and d so that the function f(x)=ax^3+bx^2+cx+d has its first derivative equal to 4 at the point (1,0) and its second derivative equal to 5 at the point (2,4)

2. Relevant equations

3. The attempt at a solution
I found the first and second derivative
f'(x)=3ax^2+2bx+c
f''(x)=6ax+2b

I set
5=12a+2b
I also set
4=3a+2b+c
I get stuck trying to find the two different variables when working with the second derivative first. I know I have to substitute for the unknowns, but I don't know where to start.

2. Apr 19, 2015

### paisiello2

Tricky problem but if a function f(x) has a derivative at some specific point then what can you say about f(x)?

3. Apr 19, 2015

### MrJamesta

That f(x) is continuous at that specific point?

4. Apr 19, 2015

### paisiello2

Yes, that's true, but I am thinking even more obviously than that?

5. Apr 19, 2015

### SammyS

Staff Emeritus
@MrJamesta

What is f(1) ?

6. Apr 19, 2015

### paisiello2

You tell me.

7. Apr 20, 2015

### MrJamesta

Oh, it's an x intercept.

8. Apr 20, 2015

### paisiello2

No, it's not.

f(1)=?

You have 4 unknowns so you need 4 equations to solve this. You came up with two of them. What are the other two? It's pretty obvious.

9. Apr 20, 2015

### Staff: Mentor

Just to be clear, and to reduce confusion on the part of the OP, 1 is an x-intercept.

10. Apr 20, 2015

### paisiello2

Well, what is an x-intercept? I think it is the value of the function when x=0. But f(1) is the value of the function when x=1. So it is not an x-intercept.

Regardless, it is irrelevant to solve the problem. What are the other two equations?

11. Apr 20, 2015

### Staff: Mentor

No, that's the y-intercept, a point on the y-axis.
But your reply to the OP was incorrect, possibly steering him/her in the wrong direction.

12. Apr 20, 2015

### Staff: Mentor

To get back to the original question:
Right. Can you use it to find another equation?

13. Apr 20, 2015

### MrJamesta

I found
0=a+b+c+d
4=8a+4b+2c+d

14. Apr 20, 2015

### SteamKing

Staff Emeritus
Now, use the other two equations and solve for the unknown coefficients.