Applications of the Derrivative

[cv2yanks13]

f(x)= x^4+2x^3

Show how to find x intercepts
Show how to find critical points
Make a detaled derivative chart and use it to determine the intervals where f(x) is increasing or decreasing.. and to identify any local maximum and minimum values
Show how to find the possible inflection points.
Make a detailed second derivative chart,and use it to determine the intervals where f(x) is concave up or concave down.. and to identify the actual inflection points...

And sketch a detailed graph of this funciton.

I'm asking this question so I can FULLY understand all of the concepts.. .this isn't a homework problem... and I won't receive credit for it... I'm just a guy who sucks at math... and wants to learn Math adequately enough to get a good grade in calc...

please help me out guys... i want to learn this !!

 

[BigGlenntheHeavy]

\(\displaystyle cv2yanks13, \ I \ am \ beginning \ to \ think \ that \ you \ mistake \ kindness \ for \ stupidity \ and\)

\(\displaystyle I \ don't \ like \ looking \ stupid. \ If \ you \ have \ come \ this \ far \ in \ math, \ then \ I suggest \ you \ start\)

\(\displaystyle attending \ class \ instead \ of \ waiting \ to \ the \ last \ minute \ and \ expect \ us \ to \ pull \ your \ chestnuts\)

\(\displaystyle \ out \ of \ the \ fire.\)