# Thread: Help with finding the unkowns

1. ## Help with finding the unkowns

Let f(x) = ax^4 + bx^3 + cx^2 + dx + e be the equation of the graph.
a,b,c,d and e are the unknowns.

Then 5 equations are:
f(0)=150
f(60)=30
df/dx (60) = 0
df/dx (180) = 0
df/dx (300) = 0

I'm not 100 percent sure on how to approach this. If anyone could give me a kick in the right direction it would be greatly appreciated.

2. Originally Posted by fetget
Let f(x) = ax^4 + bx^3 + cx^2 + dx + e be the equation of the graph.
a,b,c,d and e are the unknowns.

Then 5 equations are:
f(0)=150 ... tells you e = 150
f(60)=30 ... a(60^4) + b(60^3) + c(60^2) + d(60) + 150 = 30
df/dx (60) = 0 ... 4a(60^3) + 3b(60^2) + 2c(60) + d = 0
df/dx (180) = 0 ... same drill as above except w/ x = 180
df/dx (300) = 0 ... ditto w/ x = 300

solve for a, b, c, and d
...

3. Originally Posted by fetget
Let f(x) = ax^4 + bx^3 + cx^2 + dx + e be the equation of the graph.
a,b,c,d and e are the unknowns.

Then 5 equations are:
f(0)=150
f(60)=30
df/dx (60) = 0
df/dx (180) = 0
df/dx (300) = 0

I'm not 100 percent sure on how to approach this. If anyone could give me a kick in the right direction it would be greatly appreciated.

$\displaystyle f(0)=150$ into $\displaystyle f(x) = ax^4 + bx^3 + cx^2 + dx + e$ gives $\displaystyle 150 = a(0)^4 + b(0)^3 + c(0)^2 + d(0) + e$

Do you follow? Can you simplify this?

4. I understand how to get e=150 but I don't know how to work out a,b,c,d.
Do you have to use simultaneous equations by eliminating the unknowns??

5. Originally Posted by fetget
I understand how to get e=150 but I don't know how to work out a,b,c,d.
Do you have to use simultaneous equations by eliminating the unknowns??
that's how.

6. So would I use the 3 differentiated equations to work it out.
$\displaystyle 4a(60^3) + 3b(60^2) + 2c(60) + d = 0$ Equation (1)
$\displaystyle 4a(180^3) + 3b(180^2) + 2c(180) + d = 0$ Equation (2)
$\displaystyle 4a(300^3) + 3b(300^2) + 2c(300) + d = 0$ Equation (3)

From there I would need to eliminate an unknown.
Could you help me in getting one of the unknowns for eg. d because I think that one is the easiest.

7. you forgot an equation ... $\displaystyle f(60) = 30$

$\displaystyle a(60^4) + b(60^3) + c(60^2) + d(60) + 150 = 30$

8. You need to use 4 equations because you have 4 unknowns