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)

calculus 
Steve
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
Respond to this Question
Similar Questions

MathCalculus (check please)
FOr the function f(x)=x^2e^x Find the critical points, increasing decreasing, first and second derivative and concavity I am having trouble finding the concavity >_< First derivative: xe^x(x+2) Second : e^x(x^2+4x+2) Critical … 
Calculus
For y=(1/4)x^4(2/3)x^3+(1/2)x^23, find the exact intervals on which the function is a. increasing b. decreasing c. concave up d. concave down Then find any e. local extreme values f. inflection points  I thought it'd be better … 
Math
I need help... I don't need the answer just how I would figure this out. Identify the hypotenuse of the triangle by giving its letter. It is a triangle with the left and bottom lines of the triangle as a right angle. The longest line … 
Calculus
Hi! I am having trouble figuring out the derivative of ln[sin^2(x)+3]........... If it weren't for the "3" I know I could just "move" the exponent of 2 from sin^2 to in front of the ln,....but because of the 3 I can't do this....So … 
Calculus
1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[4,2]. If Rolle's Theorem can be applied, … 
calculus
find the points of inflection and discuss the concavity of the graph of the function f(x) = sin x + cos X 0<x< 2pie 
calculus
Find any relative extrema and any points of inflection if they exist of f(x)=x^2+ ln x^2 showing calculus. Please show work in detail so I can follow. Thanks. The answer is no relative max or min and the points of inflection are (1,1) … 
Calculus
f(x)= x/(1+x)^2 c) find the intervals of concavity and the inflection points. My answers: f is concave downward on ( infinity, 2) and concave upward on (2, infinity). Inflection point: ( 2, 2/9) 
calculus
Given the function f(x)=1/4 x^4  3/2 x^2 a. discuss the relative maxima, minima relative b. determine where f is increasing and where f is decreasing c. Find the points of inflection. d. Discuss the concavity 
Math Need Help..
I'm having trouble with a question from one of my math assignments and it's driving me crazy. Its: 2/5x  9 < 9/10 (twofifths and ninetenths) I tried doing it a few times, it might be easier than it looks and I just don't understand. …