Properties of the curve

label Calculus
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f(x) = 2x^3 + 3x^2 - 180x - 2

When is the function decreasing?

When is the function increasing?

What is the local maximum of the function?



Apr 8th, 2015

decreasing: (-6,5)

increasing: (negative infinity,-5), (5,infinity)

local maximum: x=-6, y=754

Apr 8th, 2015

could you double check where it is increasing? this answer was not correct

Apr 8th, 2015

checking

Apr 8th, 2015

increasing: (negative infinity,-6), (5,infinity)

sooo sorry, my careless mistake....

Apr 8th, 2015

You can get the answer by taking the derivative of the function.

y'=6x^2+6x-180=x^2+x-30=(x-5)(x+6)

let y'>0, function is increasing at x>5, x<-6

let y'<0, function is decreasing at -6<x<5

let y'=0, we get the critical point, x=5, x=-6. 

By looking at the graph, or analyze from the increasing/decreasing of the function above, we get local maximum at x=-6, local minimum at x=5

If you have any other questions let me know. Please add me as a tutor if you want, I would like to talke further with you regarding something..thank you. 

Apr 8th, 2015

Thank you so much. It really helps to have it explained like that. Also, I added you as a tutor.

Apr 8th, 2015

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