OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

@IMStuck

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

lol thank ya

4 years ago
OpenStudy (anonymous):

please help

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (zarkon):

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

4 years ago
OpenStudy (zarkon):

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

4 years ago
OpenStudy (zarkon):

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

4 years ago
OpenStudy (zarkon):

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

4 years ago
OpenStudy (anonymous):

one second let me look again

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (zarkon):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

nevermind

4 years ago