Question

i need help with
a.) determining where the function is increasing or decreasing.

and
b.) determine where the function is concave up or concave down.

Answer 1

t-ln(t)

Answer 2

f(x)=t-ln(t)

Answer 3

you can use the first derivative test to find part a.
2nd derivative test for part b

Answer 4

well i got 1-1/t for the first derivative but im not sure if thats correct

Answer 5

differentiate the function
- as dockworker said

Answer 6

perhaps you should post the original equation

Answer 7

f(x)= t - ln(t)

Answer 8

that is the original equation

Answer 9

dont we need to know the range of values involved here?

Answer 10

so you need to find the critical numbers (the zeros of the first derivative and also those numbers that make the first derivative undefined)

Answer 11

it dosnt give me a range of values

Answer 12

right

Answer 13

so t=0, t=1 are your critical numbers

Answer 14

how did you get zero and one?

Answer 15

test a sample from the 3 intervals these 2 critical numbers divide the domain into
(-infinity,0), (0, 1), (1, infinity)

Answer 16

when t=0, the derivative is undefined

Answer 17

the first derivative is the slope of the tangent line. if the slope is positive in one of these intervals, the function is increasing in that interval. if negative, decreasing in that interval

Answer 18

i'm sorry but i must go now. you should bump this question to the top to receive more help

Answer 19

you'll find the graph of this function here

http://www.wolframalpha.com/input/?i=y+%3D+t+-+ln+t

Answer 20

as you can see its concave up when t > 0
second derivative = 1 / t^2 which is positive (because t^2 must be postive) and so this is a minimum whch is concave up