Question

find the x and y intercepts of 3x^(2/3)-2x. show all work please

Answer 1

\[y = 3x ^{2/3} - 2x\]
y intercept is when x = 0, so y intercept is y = 0
x intercept is when y = 0 giving
\[0 = 3x ^{2/3} - 2x = x(3x ^{-1/3} - 2)\]
so x = 0 or \[3x ^{-1/3} - 2 = 0\]
2nd solution can be re-written as \[3x ^{-1/3} = 2\]
\[3 = 2x ^{1/3}\]
\[x ^{1/3} = 3/2\]
\[x = (3/2) ^ {3} = 27/8 = 3.375\]
so x intercepts are x = 0 and x = 3.375