1. ## finding critical numbers

I am stuck on the problem :
Find the Critical Numbers of F(x)= 2^(2x-5)-2^(x+1)
I differentiated and got to :
F'(x)=(ln(2)*4^x)/(16)-2ln(2)*2^x
I am not sure what to do next?

2. Originally Posted by sydewayzlocc
I am stuck on the problem :
Find the Critical Numbers of F(x)= 2^(2x-5)-2^(x+1)
I differentiated and got to :
F'(x)=(ln(2)*4^x)/(16)-2ln(2)*2^x
I am not sure what to do next?
A number $\displaystyle a$ in the domain of a given function $\displaystyle f$ is called a critical number of $\displaystyle f$ if $\displaystyle f '(a) = 0$ or $\displaystyle f'$ is undefined at $\displaystyle x = a$.

so, solve for $\displaystyle f'(x)=0$.

3. yes thank you I realize that a critical number is when f'(x) is 0 or undefined, and the answer I got for the derivative is what the calculator gave me for d/dx of f(x). I am just unsure how to go about solving for x with the natural logs.

4. Originally Posted by sydewayzlocc
yes thank you I realize that a critical number is when f'(x) is 0 or undefined, and the answer I got for the derivative is what the calculator gave me for d/dx of f(x). I am just unsure how to go about solving for x with the natural logs.
$\displaystyle \frac{d}{dx} (2^{2x-5} - 2^{x+1}) = 2^{2x-4} \mbox{log}(2)-2^{x+1} \mbox{log}(2)$

solving $\displaystyle f'(x) = 0$ gives x=5.