Question

Application of Differentiation ( max and min values)
Help me through these steps to find max and min.... f(x)= x/x^2+1, [0,2]

Answer 1

The max/min will occur at an end point of your interval or at an interior point where \[f^{\prime}(x)=0\]

Answer 2

what is f(x) in this case?

Answer 3

is it\[f(x)=\frac{x}{x^2+1}\]?

Answer 4

it is difficult to tell by the way you wrote it...

Answer 5

yes but also [0,2]

Answer 6

yes, I get that your are looking for absolute max/min on the interval [0,2]

Answer 7

okay so first we need \[f^\prime(x)\]

Answer 8

do you have it ? or do we need to figure it out?

Answer 9

\[f^\prime(x)=\frac{1-x^2}{(x^2+1)^2}\]

Answer 10

yes its 1(x^2+10 * x(2x+1) / (x^2+1)^2 right....i dont know how to write it out how you are

Answer 11

you can use the equation writer button or encode directly with Latex as I am, but its okay to use plain text as long as you use grouping symbols to include all of the numerator and denominator

Answer 12

your derivative does not look correct

Answer 13

\[f^\prime(x)=\frac{(1)(x^2+1)-x(2x)}{(x^2+1)^2}\]

Answer 14

i so knew that but rushing

Answer 15

\[=\frac{x^2+1-2x^2}{(x^2+1)^2}\]

Answer 16

okay, cool

Answer 17

then we can move forward

Answer 18

since the denominator is the sum of positive numbers the derivative of this function is never undefined so we just need to find where it equals 0

Answer 19

setting the numerator equal to zero we get \[x=\pm 1\]

Answer 20

habachuchu

Answer 21

2x^2 / x^2+1 is what i get next

Answer 22

now note that \[x=-1\] is not in the interval [0,2] so we do not need to consider it for this problem

Answer 23

now we just evaluate \[f(0),f(1),f(2)\] and compare

Answer 24

\[f(0)=0\]\[f(1)=\frac{1}{2}\]\[f(2)=\frac{2}{5}\]

Answer 25

so on the interval [0,2] our function has an absolute max of 1/2 and an absolute min of 0

Answer 26

okay i get the last part you did but after i get the x^2+1-2x^2 / (x^2+1)^2 i get confused on what you mean

Answer 27

the numerator of your derivative is 1-x^2 after you "clean it up"

Answer 28

thats the thing where i really need help my college algebra suck i dont know how to get that after i get 2x^2 / x^2+1

Answer 29

x^2+1-2x^2=1-x^2

Answer 30

okay i can see that i just thought you would canceled the numerator x^2+1 with the denominator and the square would cancel