1) For the function below, find a) the critical numbers; b) the open intervals w
ID: 3018684 • Letter: 1
Question
1)
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 a) Find the critical number(s). Select the correct choice below and, if necessary, fil in the answer box to complete your choice. O A. The critical number(s) is are [ Type an integer or a simplified fraction. Use a comma to separate answers as needed) B. There are no critical numbers. b) Determine the interval(s) on which the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. List any interval(s) on which the function is increasing. (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed) O B. The function is never increasing c) Determine the interval(s) on which the function is decreasing Select the correct choice below and, if necessary, fil in the answer box to complete your choice A. List any interval(s) on which the function is decreasing. Type your answer in interval notation. Simplify your answer Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. The function is never decreasing. Click to select and enter your answerls).
Explanation / Answer
given f(x)=(x2+9), domain is (-,)
=> f '(x)=(1/2(x2+9))(2x+0)
=> f '(x)=(x/(x2+9))
a)
for critical numbers, f '(x)=0
=>(x/(x2+9))=0
=>x=0
critical number is 0
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b)
function increases when f '(x)>0
=>(x/(x2+9))>0
=>x>0
function is increasing in (0,)
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c)
function decreases when f '(x)<0
=>(x/(x2+9))<0
=>x<0
function is decreasing in (-,0)
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