Suppose the derivative of a function: On what interval(s) is f increasing?

Question

Suppose the derivative of a function f is f' (x) = (x−3)² (x+ 3)⁷ (x−5)⁸ . On what interval(s) is f increasing?

Answer 1

f is increasing when f' >0

(x-3)^2 is always positive, (x-5)^8 is always positive

(x+3)^7 is positive when x+3 is positive, when x>-3

f is decreasing from negative infinity to -3 and increasing from x=-3 to x= + infinity

f is increasing on the interval (-3, infinity)