which one

in Calculus Answers by Level 2 User (1.4k points)
reopened by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Best answer

dp/dx=(x²+20)-2x(x-4))/(x²+20)²=0 at an extremum, dp/dx=1/(x²+20)-2x(x-4)/(x²+20)².

That is, x²+20-2x²+8x=0, -x²+8x+20=0=-(x-10)(x+2). The critical points are at x=10 and -2.

d²p/dx²=-2x/(x²+20)²-[(x²+20)²(4x-8)-4x(2x²-8x)(x²+20)]/(x²+20)⁴.

When x=10 this is -20/120²-[120²(32)-40(120)²]/120⁴=-20/120²+8/120²<0 (maximum), and p(10)=6/120=1/20.

When x=-2 it’s 4/24²-[24²(-16)+8(24²)]/24⁴>0 (minimum), and p(-2)=-6/24=-¼.

Max at (10,1/20); min at (-2,-¼). If the critical points are the maximum and minimum then all the answer options are incorrect, the closest being answer a. But the points in this answer option are not even on the curve!

by Top Rated User (804k points)
selected by

Related questions

1 answer
asked Nov 28, 2011 in Calculus Answers by TDP Level 1 User (740 points) | 370 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,844 questions
91,601 answers
2,224 comments
15,916 users