Unknown Constants Possible Derivative Problem

**r2d2** · October 14th 2009, 05:59 AM

If $h(x) = x^n / k$ and $k$ is a nonzero constant and $n$ is an integer, find the values of $k$ and $n$ 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!

**Defunkt** · October 14th 2009, 06:16 AM

Originally Posted by r2d2

If $h(x) = x^n / k$ and $k$ is a nonzero constant and $n$ is an integer, find the values of $k$ and $n$ 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:

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

So find the derivative, substitute it into the proper equation and solve for n,k.

**r2d2** · October 14th 2009, 06:33 AM

so would the derivative be $h'(x)= (k)(nx^(n-1)) - x^n(1) / k^2$

**Defunkt** · October 14th 2009, 08:06 AM

Originally Posted by r2d2

so would the derivative be $h'(x)= (k)(nx^(n-1)) - x^n(1) / k^2$

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

The derivative will be:

$h'(x) = \frac{nx^{n-1}}{k}$

**r2d2** · October 14th 2009, 08:07 AM

Yup I solved this. Thank you for your help!!

Thanks +1

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