# Thread: Determine the values of a and b for the function.

1. ## Determine the values of a and b for the function.

Determine the values of a and b for the function f(x)=ax^3 +bx^2 +3x -2 given that f(2)=10 and f'(-1)=14.

Where would I start?

2. Originally Posted by kmjt
Determine the values of a and b for the function f(x)=ax^3 +bx^2 +3x -2 given that f(2)=10 and f'(-1)=14.

Where would I start?
$\displaystyle f(2) = 10$ ...

$\displaystyle 10 = a(2)^3 + b(2)^2 + 3(2) - 2$

do the same for $\displaystyle f'(-1) = 14$ ... then solve the system of equations for $\displaystyle a$ and $\displaystyle b$

3. f(x)=ax^3 +bx^2 +3x -2

f'(x) = 3ax^2 +2bx +3 -2

14 = 3a(-1)^2 +2b(-1) +3

If thats what you mean. What would I do now? I'm not really sure how to isolate a or b.

4. Originally Posted by kmjt
f(x)=ax^3 +bx^2 +3x -2

f'(x) = 3ax^2 +2bx +3 -2

14 = 3a(-1)^2 +2b(-1) +3

If thats what you mean. What would I do now? I'm not really sure how to isolate a or b.
You have two equations and two variables. Solve them simultaneously.

$\displaystyle 10 = a(2)^3 + b(2)^2 + 3(2) - 2$

$\displaystyle \Rightarrow 8a+4b-6=0$ $\displaystyle \rightarrow\color{red}{(1)}$

--------------------------------------------------------

$\displaystyle 14 = 3a(-1)^2 +2b(-1) +3$

$\displaystyle \Rightarrow 3a -2b - 11=0 \Rightarrow a= \frac{2b+11}{3}$ $\displaystyle \rightarrow\color{red}{(2)}$

--------------------------------------------------------

Now sub $\displaystyle \color{red}{(2)}$ into $\displaystyle \color{red}{(1)}.$

$\displaystyle \Rightarrow 8(\frac{2b+11}{3})+4b-6=0$

5. Got it thanks