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 $a$ in the domain of a given function $f$ is called a critical number of $f$ if $f '(a) = 0$ or $f'$ is undefined at $x = a$.

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

$\frac{d}{dx} (2^{2x-5} - 2^{x+1}) = 2^{2x-4} \mbox{log}(2)-2^{x+1} \mbox{log}(2)$
solving $f'(x) = 0$ gives x=5.