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- d^2y/dx^2 = 2 which is positive...
Algebra/d^2y/dx^2 = 2 which is positive...
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Question
d^2y/dx^2 = 2 which is positive hence the turning point is a minimum,
can you find the turning points for the following curves and distinguish between them ?
a) x = 0(6-0)
b) x = 8t + 1/2t^2
(the ''0'' in question a) has a horizontal line through the middle)
a) I'll use 't' instead of '0'...so, x=t(6-t)=6t-t^2
dx/dt=6-2t=0 ==> t=3, with x''=-2, thus t=3
corresponds to a maximum (esp. since the graph is
an upside-down parabola)!
b) x'=8+t=0 ==> t=-8, with x''=1...thus t=-8 corresponds
to a minimum (esp. since the graph is parabola)!
Abe
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Answers by Expert:
Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience
Over 15 years teaching at the college level.
Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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