# Unknown Constants Possible Derivative Problem

• Oct 14th 2009, 05:59 AM
r2d2
Unknown Constants Possible Derivative Problem
If $\displaystyle h(x) = x^n / k$ and $\displaystyle k$ is a nonzero constant and $\displaystyle n$ is an integer, find the values of $\displaystyle k$ and $\displaystyle n$ so that where x=2, the value of h(x) is equal to 8 and the slope of the graph of the same function is -4

Would i first solve the derivative and work from there? Thanks!
• Oct 14th 2009, 06:16 AM
Defunkt
Quote:

Originally Posted by r2d2
If $\displaystyle h(x) = x^n / k$ and $\displaystyle k$ is a nonzero constant and $\displaystyle n$ is an integer, find the values of $\displaystyle k$ and $\displaystyle n$ so that where x=2, the value of h(x) is equal to 8 and the slope of the graph of the same function is -4

Would i first solve the derivative and work from there? Thanks!

You will need to solve the following equation system:

$\displaystyle (1) \ h(2) = 8 \Rightarrow \frac{2^n}{k} = 8$
$\displaystyle (2) \ h'(2) = -4$

So find the derivative, substitute it into the proper equation and solve for n,k.
• Oct 14th 2009, 06:33 AM
r2d2
so would the derivative be $\displaystyle h'(x)= (k)(nx^(n-1)) - x^n(1) / k^2$
• Oct 14th 2009, 08:06 AM
Defunkt
Quote:

Originally Posted by r2d2
so would the derivative be $\displaystyle h'(x)= (k)(nx^(n-1)) - x^n(1) / k^2$

No. k is a constant, you don't treat it as a function of x.

The derivative will be:

$\displaystyle h'(x) = \frac{nx^{n-1}}{k}$
• Oct 14th 2009, 08:07 AM
r2d2
Yup I solved this. Thank you for your help!!

Thanks +1