# finding critical numbers

#### 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?

#### harish21

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 $$\displaystyle f'(x)=0$$.

#### 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.

#### harish21

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.