finding critical numbers

Apr 2010
53
0
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?
 
Feb 2010
1,036
386
Dirty South
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 \(\displaystyle f'(x)=0\).

By the way, is your differentiation complete? Your answer doesn't seem correct
 
Apr 2010
53
0
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.
 
Feb 2010
1,036
386
Dirty South
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.