# 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?
$f(2) = 10$ ...

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

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

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.

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

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

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

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

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

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

5. Got it thanks