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Thanks for taking my question, I really appreciate the assistance you provide, a very generous thought!

My question is:

Given y=2x^(3)+5x^(2)-4x

In what intervals is the function concave up or down, and what are the inflection points (x=...)

Let dy/dx = 6x^2 + 10x - 4 = 0,

then3x^2 + 5x - 2 = 0

x = 1/3 or x = -2.

Now d^2y/dx^2 = 12x +10 = 0 for4 infl. So x = -10/12 = -5/6

and y = -2(5/6)^3 + 5(5/6)^2 + 4*5/6.

F"(1/3) = 14 > 0 Curve is concave upward.

To find the interval test the sign of f"(x) for x > -5/6 and x <5/6.

When f'(x) is + curve is concave upward, when - curve is concave downward,

Calculus

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