Question

f(s) = 2s^3+18s^2+5

(need help with the concave upward)

f(s) is increasing for s < -6
f(s) is decreasing for -6 < s < 0
f(s) is increasing for s > 0
f(s) is concave downward for s < -3
f(s) is concave upward for s > ?
The relative maximum is at (-6, 221)
The relative minimum is at (0, 5)
The inflection point is at (-3, 113)

Answer 1

concave upward is any positive value of the second derivative, and it gives you a local maximum. If second derivative is 0 you have an inflection point.

a cubic graph only has at most one max and one min.

does that make sense?

Answer 2

So I can use any number I choose?

Answer 3

it is concave upward from any where from the inflection point to +infinity. so long as you havent limited the domain.

Answer 4

the graph looks like a modified "N" shape. Anything to the right of inflection is concave up and anything to the left of inflection is concave down. The minimum is the bottom of the "bowl" on the right of the graph, and the maximum is the top of the "bowl" on the left side of the graph. Concavity isnt just a single point.

Answer 5

unless I am wrong, but Im usually right :)

Answer 6

You are right! But I must be entering the wrong number somehwhere because all of my numbers are correct but the convave upward!