i have no clue how to do this problem. i need some help.

Given a power function of the formf(x)=ax^n, withf '(3)=18 andf '(6)=72, findnanda.

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- Oct 6th 2008, 07:23 PMjojoferni244finding values from power functions
i have no clue how to do this problem. i need some help.

Given a power function of the form*f*(*x*)=*ax^n*, with*f '*(3)=18 and*f '*(6)=72, find*n*and*a*. - Oct 6th 2008, 07:31 PMChris L T521
- Oct 6th 2008, 07:34 PMjojoferni244
actually im stuck...can you help me please

- Oct 7th 2008, 12:52 PMChris L T521
Note that 4*18=72

So we can see that the last equation is $\displaystyle 18=\tfrac{1}{4}\cdot6^{n-1}an$

Thus, $\displaystyle \tfrac{1}{4}6^{n-1}an=3^{n-1}an\implies \tfrac{1}{4}6^{n-1}=3^{n-1}\implies \tfrac{1}{4}=\frac{3^{n-1}}{6^{n-1}}\implies \tfrac{1}{4}=\left(\tfrac{3}{6}\right)^{n-1}$ $\displaystyle \implies \tfrac{1}{4}=\left(\tfrac{1}{2}\right)^{n-1}\implies \tfrac{1}{4}=\left(\tfrac{1}{2}\right)^{-1}\left(\tfrac{1}{2}\right)^n\implies \tfrac{1}{8}=\left(\tfrac{1}{2}\right)^n$

Can you take it from here? You will find an integer value for n.

Then plug this into either equation and solve for a.

--Chris