calculus
posted by rachel .
im having so much trouble figuring out how to get these answers. i already know the answers i just need to figure out how to get them...
directions: find the points of inflection and discuss the concavity of the graph of the function...
1. f(x)=(1/2)x^4+2x^3
2. f(x)=x^36x^2+12x
3. f(x)=(1/4)x^42x^2
4. f(x)=2sinx+sin2x, [0,2ð)

1.
f = 1/2 x^4 + 2x^3
f' = 2x^3 + 6x^2
f'' = 6x^2 + 12x
f' = 0 at x=0,0,3 so the possible mins/maxes are there
f'' = 0 at 0,2 so the inflection is there.
At x=0, f'=0 and f''=0, so not a min/max  inflection
At x=3, y'' > 0, so concave up (min)
Proceed similarly with the others.
rechneronline . de is a good grapher