







f(x)= (e^x) / [(e^x)+(ex^2)] 
20091110 

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,
natalie Answered by Chris Fisher and Harley Weston. 





Graphing y=(4x^2)^5 
20091025 

From natalie: I want to graph the curve of y=(4x^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,
natalie Answered by Harley Weston. 





Concavity and the second derivative 
20081015 

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^24)/(2x^2)
however, using the quotient rule again I can't seem to solve it (concavity):
f'''(x)=[(2x)(2x^2)(x^24)(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 
20071122 

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 + 1 Answered by Harley Weston. 





Concavity of f(g) 
20011025 

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 
20001022 

From Alex: the question is: on what interval is f(x)=(x^{2})(e^{x})? ive found the 2nd derivative which is e^{x}(x^{2}+4x+2) and i did the quadratic to get 22^{0.5} and 2+2^{0.5}, but i dont know what the interval is. Answered by Harley Weston. 

