Question
Determine the concavity for f(x)= 4/x^2-1
I took the second derivative and solved for zeros. I got x=-1 and x=1. However when plugged into the orig. equation this results in 4/0 (undefined). Does this mean there is no concavity?
I took the second derivative and solved for zeros. I got x=-1 and x=1. However when plugged into the orig. equation this results in 4/0 (undefined). Does this mean there is no concavity?
Answers
if f = 4/(x^2-1)
f'' = 8(3x^2+1)/(x^2-1)^3
f'' is never zero.
f'' is discontinuous at x=1 and -1, and changes sign there
so, f ix concave down for |x|<1 and concave up for |x|>1
f'' = 8(3x^2+1)/(x^2-1)^3
f'' is never zero.
f'' is discontinuous at x=1 and -1, and changes sign there
so, f ix concave down for |x|<1 and concave up for |x|>1
Related Questions
Find the concavity and min and max for f(x) = x*sqrt(x^2+36) defined on the interval [-4, 7]?
Determine the concavity and find the points of inflection.
y=2cosx + sin2x 0≤x≤2pi
y'=-2sinx + 2co...
Find the interval of concavity for f(x)=e^x/(5+e^x)?
f'=[5*e^x ]/ [5+e^x]^2 & f"=[5*e^x ][5-e^x]/...
The section is on concavity and the second derivative test, the question is:
Determine all signific...
Determine the concavity in the graph of f (x) = -4x^3 + 8x^2 + ax + b, where a and b are real number...
Determine the concavity of
f(x)=xlnx
I end up with
F''(x)=1/x, where it would be concave up w...
What does it mean for concavity of the original graph if there is an asymptote in the f'' graph?
What is the concavity of the function?
Present the concavity test and explain how to use
�
′
′
(
�
)
f
′′
(x) to determine conc...
What is the concavity of the quadratic function f(x) = x^2 + 5x?