Thread: 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?

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 in the domain of a given function is called a critical number of if or is undefined at .

so, solve for .

By the way, is your differentiation complete? Your answer doesn't seem correct

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.

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.

solving gives x=5.