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?
You have two equations and two variables. Solve them simultaneously.
$\displaystyle 10 = a(2)^3 + b(2)^2 + 3(2) - 2$
$\displaystyle \Rightarrow 8a+4b-6=0$ $\displaystyle \rightarrow\color{red}{(1)}$
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$\displaystyle 14 = 3a(-1)^2 +2b(-1) +3$
$\displaystyle \Rightarrow 3a -2b - 11=0 \Rightarrow a= \frac{2b+11}{3}$ $\displaystyle \rightarrow\color{red}{(2)}$
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Now sub $\displaystyle \color{red}{(2)}$ into $\displaystyle \color{red}{(1)}.$
$\displaystyle \Rightarrow 8(\frac{2b+11}{3})+4b-6=0$