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Quandaries & Queries
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 Topic: concavity
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 f(x)= (e^x) / [(e^x)+(ex^2)] 2009-11-10 From natalie:I'm trying to graph the function, f(x)= (e^x) / (e^x)+(ex^2) [e to the x divided by e to the x plus e times x squared] I know that there aren't any vertical asymptotes, but is there a horizontal asymptote? and also, I'm stuck on finding the concavity for this graph. I tried to find f "(x), but it came out to be really long and I am not sure how to find the x values for f "(x) without using a graphic calculator. thanks, natalieAnswered by Chris Fisher and Harley Weston. Graphing y=(4-x^2)^5 2009-10-25 From natalie:I want to graph the curve of y=(4-x^2)^5 without using a graphing calculator. To do this, I'm suppose to find: domain, y and x intercepts, asymptotes, intervals of increase/decrease, local max/min, concavity and points of inflection. I got all the way to the step where I'm solving the concavity and I'm stuck. I found the f"(x) and it came out to be really large polynomial. I want to know how I can solve for the x of f"(x) without the use of a graphing calculator, when the polynomial has x^6 and x^8. Thank you so much, natalieAnswered by Harley Weston. Concavity and the second derivative 2008-10-15 From Christina:I'm having trouble solving for a second derivative for the following graphing question. f(x) = (X^2+2x+4)/2x using the quotient rule, I found: f'(x) = (x^2-4)/(2x^2) however, using the quotient rule again I can't seem to solve it (concavity): f'''(x)=[(2x)(2x^2)-(x^2-4)(4x)]/[(2x^2)^2] f''(x)=[(4x^3-(4x^3 -16x)]/4x^4 f''(x)=16x/4x^4 f''(x)=4/x^3 and making the equation equal to zero result in 0=4 which doesn't seem to make sense...Answered by Penny Nom. A curve sketch 2007-11-22 From Ahson:Find critical points, determine the monotonicity and concavity and sketch a graph of f(x) with any local maximum, local minimum and inflection points labeled: 1. f(x) = x^4 - x^3 - 3x^2 + 1Answered by Harley Weston. Concavity of f(g) 2001-10-25 From Troy:Suppose f & g are both concave upward on (-infinity,infinity). Under what condition on f will the composite function h(x)= f(g(x)) be concave upward? Answered by Walter Whiteley. Concavity 2000-10-22 From Alex:the question is: on what interval is f(x)=(x2)(ex)? ive found the 2nd derivative which is ex(x2+4x+2) and i did the quadratic to get -2-20.5 and -2+20.5, but i dont know what the interval is.Answered by Harley Weston.

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