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 .
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