Question

Find the intervals of increase or decrease:
C(x)=x^(1/3)(x+4)

Answer 1

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

Answer 2

This doesn't seem right though and I'm pretty sure it has something to do with satan's fractional exponents. Can someone show me where I went wrong?

Answer 3

derivative of x+4 is not x

Answer 4

your first line