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Math Help - finding critical numbers

  1. #1
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    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?
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by sydewayzlocc View Post
    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.

    By the way, is your differentiation complete? Your answer doesn't seem correct
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  3. #3
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    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.
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by sydewayzlocc View Post
    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.
    \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.
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