Question

C(x) = x1/3(x + 4)
(a) Find the interval of increase. (Enter your answer using interval notation.)

Answer 1

\[C(x)=x ^{1/3}(x+4)\]

Answer 2

\[C'(x)=x ^{1/3}(1)+(x+4)1/3(x ^{-2/3})\]

Answer 3

\[C'(x)=x ^{-2/3}(x+((x+4)/3)\]

Answer 4

\[C'(x)=x ^{-2/3}[(3/3)x+x/3+4/3]\]

Answer 5

x^-2/3[4x/3+4/3]

Answer 6

\[(4/3)x^{2/3}[x+1]\]=0

Answer 7

meaning x=0 and x=-1?
but then when i plug negative two into C' I get a positive out which is not the right anser

Answer 8

@IMStuck

Answer 9

@Dscdago @Ail.A @MaimiGirl @superdude123 @superdude123 @cutepochacco can any of u guys help. he's been waiting forever.

Answer 10

lol thank ya

Answer 11

please help

Answer 12

this sucks im getting the same thing everytime i dont know what im missing

Answer 13

how do you get a positive when you plug in -2?

Answer 14

the derivative is

\[\frac{4}{3}\frac{x+1}{x^{2/3}}\]

Answer 15

looks like you lost the negative on your exponent towards the end

Answer 16

\[\Large\left.\frac{4}{3}\cdot\frac{x+1}{x^{2/3}}\right|_{x=-2}=\frac{4}{3}\cdot\frac{-2+1}{(-2)^{2/3}}=\frac{4}{3}\cdot\frac{-1}{4^{1/3}}<0\]

Answer 17

one second let me look again

Answer 18

so when you have an exponent
thats a fraction.....you do the exponents numerator first and then the denomenator? when I put -2^(2/3) in my calculator it gives me a negative number

Answer 19

put in \[(-2)^{2/3}\]

Answer 20

wow. ok but now they say that for the middle interval (-1,0) its positive, but i get negative, with -.5
\[(4(-.5)-1)/3*(-.5)^(2/3)\]
\[-3/3*.629961\]

Answer 21

nevermind