For the function below, find (a) the critical numbers; (b) the open intervals wh
ID: 2891062 • Letter: F
Question
For the function below, find (a) the critical numbers; (b) the open intervals where the function is increasing and (c) the open intervals where it is decreasing f(x)-X4X - 252x-8 (a) The critical number(s) is/are 7,9 Type an integer or a simplified fraction. Use a comma to separate answers as needed.) (b) On which intervals is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice OA. Increasing on (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Simplify your answers.) OB. Never increasing Click to select and enter your answer(s) and then click Check Answer.Explanation / Answer
f(x) = (4/3)x3-4x2-252x-8
f'(x)= (4/3)*3x2-4*2x -252=4x2-8x-252
f'(x)=0
4x2-8x-252=0
4(x2-2x -63)=0
(x-9)(x+7)=0
x=-7,9
In interval (-infinity,-7)
f'(-10)=57>0
In interval (-7,9)
f(0)=-63,<0
In interval (9,infinity)
f(10)=17>0
So increasing in (-infinity,-7)U(9,infinity)
Decreasing in (-7,9)