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Calculus/Homeschooling Question

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Question
My name is John, I am homeschooling my son in Calculus, but I am having a little trouble with next week's lesson material; I was hoping a good example would help. I included a problem below, I was hoping you could solve it and briefly include your steps.

y=2x^3+5x^2-4x
Find y', as well as all the local maximums and minimums.

Thank you so much,
John

Answer
y'=6x^2+10x-4

Solving y'=0, gives  2(3 x-1) (x+2)=0...thus, x=-2 or x=1/3

y''=12x+10....y''(-2)=-14 < 0, so the graph is concave down at x=-2...thus, (-2,12) is a local maximum
y''(1/3)=14 > 0, so the graph is concave up at x=1/3...thus, (1/3,-19/27) is a local minimum.

Good?

Abe M.

Calculus

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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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