Homework Help Forum: Calculus

Posted by Z32 on Tuesday, October 27, 2009 at 1:20am.

What are the critical points of f(x)= e^x / 3+e^x?

• Calculus - Reiny, Tuesday, October 27, 2009 at 8:25am

  You have posted enough questions here to know that we need brackets to avoid confusion with these kind of fractions. I will assume you meant f(x) = e^x/(3+e^x) By the quotient rule : f'(x) = [(3+e^x)(e^x) - e^x(e^x)]/(3+e^x)^2 = 3e^x/(3+e^x)^2 set that equal to zero to find max/min points so 3e^x = 0 no solution Your function has no max or min points. take second derivative by using the quotient rule again, set that equal to zero to find any points of inflection. Some texts will include the x and y intercepts when finding "critical" points, so sub in x=0 to find the y-intercepts f(0) = e^0/(3+e^0) = 1/(3+1) = 1/4 for the x-intercept, let f(x) = 0 0 = e^x/(3+e^x) then 0 = e^x which yields no solution.

  
  

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