Calculus
posted by Ally .
Im finding local Min and max of x^2/x2
I know I take the derivative of the first one but how do i derive this one. And the second one especially don't know how to do.

Calculus 
Steve
Use the quotient rule to differentiate (not derive):
if y = f/g
y' = (f'g  fg')/g^2
so, we have
y = x^2/(x2)
y' = [(2x)(x2)  x^2(1)]/(x2)^2
= x(x4)/(x2)^2
Or, you can divide first
y = x+2 + 4/(x2)
y' = 1  4/(x2)^2
anyway, min/max is where y'=0, so x=0 or 4. (This is easiest to see looking at the first form of the solution.)
which is min, which is max?
y'' = 8/(x2)^3
y''(0) = 1, so y is concave down (max)
y''(4) = +1, so y is concave up (min)
Respond to this Question
Similar Questions

finding numbers
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? 
local min
f(x) = x^4 + ax^2 What is a if f(x) has a local minimum at x=5. How do I justify the answer. The first derivative has to be zero at x = 5. You then check what the second derivative is at x = 5. If it is positive then that's ok. In … 
Calculus
R=M^2(c/2m/3) dR/dM=CMM^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? 
calculus
(a) find the intervals on which f is incrs or decrs. (b) find the local min/max values of f. (c) find the intervals of concavity and the inflection points. f(x)=(lnx)/sqrtx I took the derivative and got 2lnx/2x^3/2 take the values … 
calc.
I'm having a lot of trouble with this problem: Sketch the graph and show all local extrema and inflections. f(x)= (x^(1/3)) ((x^2)175) I graphed the function on my graphing calculator and found the shape. I also found the first derivative: … 
calculus
Please help with this. I submitted it below but no one responded. I need the first derivative of f(x)=4(x+ then the square root to include (x(8x)), then close bracket.And then the second derivative of this to show by the second derivative … 
Calculus
Find any absolute max/min and local max/min for the function f(x)=x^34x+5 on the interval [0,5). Made sure to prove that these points are max/min values. This is what I did so far. f'(x)=3x^24=0 3x^2=4 x= 2/sqrt3 The 2/sqrt3 is … 
calculus
Find the local max/min values of f using botht the first and second derivatie test. I can do the first but I am having trouble with the second derivative. f(x)= x/(x^2+4) Help please...Thank you. 
Calculus
What is the point of inflection of the function f(x)=x^38x^2+5x+50? 
Calculus answer check
A brand new stock is also called an initial public offering. This model predicts the percent overvaluation of a stock as R(t)=9t((t3)^3/2.718) where is the overvaluation in percent and t is the time in months after the initial issue. …