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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

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

Answers by Expert:

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!

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