4x Find the absolute extrema if they exist, as well as all values of x where the

Question

4x Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)on the domain [0,4] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The absolute maximum is 1.41, which occurs at x=-/2 (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) B. There is no absolute maximum. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. ( A. The absolute minimum is , which occurs at x= O B. There is no absolute minimum (Round the absolute minimum to two decimal places as needed. Type an exact answer for the value of x where the minimum occurs. Use a comma to separate answers as needed.) Click to select and enter your answer(s) and then click Check Answer.

Explanation / Answer

f(x)= 4x/(x2+2)

f'(x) = ((x2+2)4-4x*2x)/(x2+2)2

f'(x)=(4x2+8-8x2)/(x2+2)2

=(8-4x2)/(x2+2)2

8-4x2=0

x2=2

x=-sqrt2, sqrt2

f(-sqrt2)=-4sqrt2/4=-sqrt2

f(sqrt2)=4sqrt2/4=sqrt2

f(0)=0

f(4)= 16/18= 8/9

absolute maximum is sqrt 2 at x=sqrt 2

absolute minimum is -sqrt2 at x=-sqrt2

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