Let f(x)=5x^(9/5)−45x^(4/5). Find the largest open interval(s) where f(x) increases.

Answer 1

f' = 9x^(4/5) - 36/x^(1/5)
= 9/x^(1/5) (x-4)
f increases where f' > 0, or x>4
or, where x<0