SOLUTION: Find the intervals of increase and decrease. Use the first derivatives test to find the local maxima and minima. Graph.
{{{f(x)=(x^2-1)/(x^2+1)}}}
Derivative is {{{4x/(x^2+1
Algebra.Com
Question 862385: Find the intervals of increase and decrease. Use the first derivatives test to find the local maxima and minima. Graph.
Derivative is I think
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Nope. Derivative is
}{(x^2\ +\ 1)^2})
You need to use a combination of the quotient rule and the chain rule.
1st derivative is equal to zero only when x = 0, hence the only extremum is at x = 0.
Second derivative:
^2}\ -\ \frac{2(x^2\ -\ 1)^2}{(x^2\ +\ 1)^2}\ +\ \frac{8x^2(x^2\ -\ 1)^2}{(x^2\ +\ 1)^3})
Second derivative has the value 4 (> 0) at x = 0, hence the extremum is a minimum.
The denominator of the original function has no real zeros, hence there are no vertical asymptotes to the graph of this function.
I'll leave the graphing to you, but it sort of looks like a side view of an "innie" belly button with a minimum at (0,-1) and asymptotic to y = 1 as x increases or decreases without bound.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
Find the intervals of increase and decrease. Use the first derivative test to find the... (answered by Alan3354)
Use a grapher to find all local maxima and minima and the values of x where they occur.... (answered by ewatrrr)
F(x) =1/x^2 +18x+84
a) give the domain of f in interval novation
b) find the critical... (answered by MathLover1)
Graph the function. Use the graph to find any relative maxima or minima.
f(x) = x3 +... (answered by Boreal)
For the function y = f (x) Next 3x^4 - 6x^2, determine if the graph has minima or maxima... (answered by solver91311)
Use the graph of the given function to find any relative maxima and relative minima.... (answered by ewatrrr)
CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
Use the graph of the given function to... (answered by checkley77)
graph each function. find any local maxima or minima to the nearest tenth. find intervals (answered by Fombitz)
Find the asymptotes, maxima and the minima of the following functions
f(x)= 1/( x^3 +... (answered by ewatrrr)
