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# Calculus/Homeschooling Question

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

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

Volunteer

#### 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