Question

Find the interval on which f(x)= 1+x^(3/2)-(3/2)x - 1 is increasing

so f ′′ (x)=3 /4x^(1/2)

Answer 1

where do i go from there? is the answer -1, 0 or 0,1 or -1,1

Answer 2

?

Answer 3

Let me check your differentiation

Answer 4

there is something wrong here

Answer 5

x>1

Answer 6

\[1+x^{\frac{3}{2}}-\frac{3}{2}x -1\]
is this your equation?

Answer 7

no one writes 1 - 1 so i am guessing there is a typo

Answer 8

F''[x]=
\[\frac{3}{4 \sqrt{x}}\]

Answer 9

all u need to ensure is that you have a positive gradient. so differentiate once then set that greater than 0

Answer 10

huh? lol :/

Answer 11

can you please type out the actual function?

Answer 12

you do not need the second derivative since you only need to know where it is increasing and decreasing.

Answer 13

F''[x]=\[\frac{3x^{-\frac{1}{2}}}{4 }\] is never equal to to zero which means function is either increasing through out or decreasing throughout

Answer 14

oh no! that is not right

Answer 15

second derivative tells you concavity, not intervals of increasing and decreasing. i would still like to know what the function is

Answer 16

All you need to do check the value of first derivative at any point to see whether it is positive or negative

Answer 17

the original function is f(x)= 1+x^(3/2)-(3/2)x - 1

Answer 18

the answer is x>1 man. u r confusing the poor girl

Answer 19

does it really say 1 - 1?

Answer 20

all those are possible answers that i got

Answer 21

one of them is right the others are wrong

Answer 22

\[f(x)=x^{\frac{3}{2}}-\frac{3}{2}x-1\]?

Answer 23

you wrote
\[f(x)=1+x^{\frac{3}{2}}-\frac{3}{2}x-1\] which makes little sense because no one writes plus one and minus one in the same function. i am thinking it is something else

Answer 24

it could be (3/2)(x-1) satellite.but if nt then x>1 is the answer

Answer 25

wait

Answer 26

f(x)= (1+x)^(3/2) - (3/2)x - 1

Answer 27

sorry guys :/ silly error

Answer 28

i don't know what the function is. @kboy you may be right, but how can you know since you don't know what the function is?

Answer 29

ooooooooooh

Answer 30

nw i get x>0

Answer 31

find
\[f'(x)=\frac{3}{2}\sqrt{x+1}-\frac{3}{2}\]

Answer 32

so now you find the second derivative?

Answer 33

set this equal 0 to find the critical points
no

Answer 34

Im so confused!!!

Answer 35

you just need first derivative.

Answer 36

\[\frac{3}{2}(\sqrt{x+1}-1)=0\]
\[x=0\] is your only critical point

Answer 37

you can do it that way if you like. i would not

Answer 38

thus the interval is x>0 right??????????????

Answer 39

if
\[-1<x<0\] then this thing is negative and if
\[x>1\] then it is positive. so original function was decreasing and then increasing.

Answer 40

so increasing on
\[(0,\infty)\]

Answer 41

which is x>0..why u guys confuse the girl by making it sound so complicated

Answer 42

lol. thanks to everyone though. I think I understand a little better now (:

Answer 43

you just need the sign of the derivative. but you also need to know what the original function is which is what caused the confusion;.