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Firefox File Edit View History Bookmarks Tools Window Help 10 Math 1325 Homework s M Mathway l Math Problem s x CA commodity Has A Deman... x Search webassign, net /webl Student/Assignment-Responses/submi pos 1&depa; 15484210 Most Visited Q cl f Facebook M gmail (P MyLab M Inbox jolmstead0 M Mathway Y WebAssign wolfram Mt kickass HH careers Ill Your last submission is used for your score. 2. O 0/10 points I Previous Answers LarApCalc10 2.6.508 XP. Find the second derivative. fox) x 16 X2 f"(x) solve the equation f"(x) 0. Enter your answers as a comma-separated list.) Need Help? L Read lt l Talk to a Tutor Submit Answer Save Progress Practice Another Version View Previous Question Question 2 of 10 View Next Question Home My Assignments Extension Request' WebAssign 4.0 1997-2017 Advanced Instructional Systems, Inc. All rights reserved. 12 33% Sun 6:04 PM Sy symolab My Notes Ask Your Teacher

Explanation / Answer

given

f(x) = x (16-x^2)

apply the product rule (fg)' = f' *g + f * g'

==> d/dx(x) * (16-x^2) + d/dx ((16-x^2)) x

==> (16-x^2) + x 1/2(16-x^2) d/dx (16-x^2)

==> (16-x^2) + x 1/2(16-x^2) (-2x)

==> (16-x^2) - x^2 /(16-x^2)

f'(x)==> ( -2x^2 +16 )/ (16-x^2)

f''(x) =

apply quotient rule ( f/g)' ==> f' * g - f * g' / g^2

==> d/dx ( -2x^2 +16 ) * (16-x^2) - ( -2x^2 +16 ) d/dx ( (16-x^2) ) / ( (16-x^2) )^2

==>( -4x (16-x^2) - ( -2x^2 +16 ) ( -x / (16-x^2) ) ) / ( 16 -x^2 )

==>( -4x ( 16 - x^2 ) + 16x - 2x^3 ) / (16-x^2)^(3/2)

Therefore f''(x) ==> ( 2x^3 - 48x ) / (16-x^2)^(3/2)

f''(x) = 0

( 2x^3 - 48x ) / (16-x^2)^(3/2) =0

2x^3 - 48x =0

x(2x^2 - 48 ) = 0

2x^2 = 48

== > x^2 = 24

x = 0 ,x =26 , x = - 26

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