2. find the interval(s) where the following function is increasing. graph to double check your answer.\n$y =…

2. find the interval(s) where the following function is increasing. graph to double check your answer.\n$y = \\frac{1}{3}x^{3}-5x^{2}+9x + 5$\nselect always\nselect $(1,9)$\nselect never\nselect $(-\\infty,1)\\cup(9,\\infty)$

2. find the interval(s) where the following function is increasing. graph to double check your answer.\n$y = \\frac{1}{3}x^{3}-5x^{2}+9x + 5$\nselect always\nselect $(1,9)$\nselect never\nselect $(-\\infty,1)\\cup(9,\\infty)$

Answer

Explanation:

Step1: Find the derivative

The derivative of (y=\frac{1}{3}x^{3}-5x^{2}+9x + 5) is (y'=x^{2}-10x + 9).

Step2: Solve (y'>0)

Factor (y'=x^{2}-10x + 9=(x - 1)(x - 9)). Set ((x - 1)(x - 9)>0). Using the sign - chart method: If (x<1), let (x = 0), then ((0 - 1)(0 - 9)=9>0). If (1<x<9), let (x = 5), then ((5 - 1)(5 - 9)=-16<0). If (x>9), let (x = 10), then ((10 - 1)(10 - 9)=9>0).

Answer:

((-\infty,1)\cup(9,\infty))