points of inflection

Question

hartnn · Answer

for points of inflection u equate 2nd derivative to 0...hope this helps..

anonymous · Answer

Then I see how many 0's there are?

hartnn · Answer

yes....0 is definitely one zero...but there are others u need to calculate

anonymous · Answer

i meant as in i find all of them.

anonymous · Answer

is it 6?

anonymous · Answer

There is one question I have before I will attempt this problem, I guess the above interval is in radiants?

anonymous · Answer

i dont think it matters if it is in radians or not

anonymous · Answer

$$\Large f''(x)=6x^2 \cos (2x^3)=0 $$
I am mainly asking out of curiosity, it should influence the result, but that's the derivative.

Now we can forgot about the first term because multiplication will always occur, but clearly zero is a solution to this equation.

hartnn · Answer

i got 5
0,+-1.3306,+-0.9222

anonymous · Answer

yeah i actually got 5

anonymous · Answer

According to my graph, I found 4 points where f'' change sign.
The attached graph of f''(x)

anonymous · Answer

wait so is it 4 or 5..

anonymous · Answer

because what hartnn did made sense

anonymous · Answer

four

anonymous · Answer

why is it 4?

anonymous · Answer

Look at the graph of f''

anonymous · Answer

what did you use to make that graph?

anonymous · Answer

Mathematica

anonymous · Answer

if you were to do this without a graph how woudl you do it

anonymous · Answer

http://www.wolframalpha.com/input/?i=plot++6+x^2+cos+%28+2+x^3%29+from+-+1.5+to+1.5

anonymous · Answer

why are you doing when the sign changes?

anonymous · Answer

A point of inflection x is where f changes concavity. That is where f''(x) =0 and when f'' changes sign before and after x

anonymous · Answer

So isnt f′′(x)=6x2cos(2x3)=0 have 5 x values?

anonymous · Answer

at zero f'' does not change sign.

anonymous · Answer

okay.

anonymous · Answer

so you arent supposed to just solve? you have to look at the graph

anonymous · Answer

oh yeah it doesnt change signs that makes snese

hartnn · Answer

i m sorry, my bad....i agree with eliassaab...mathematically,by making double derivative=0,we get 5 points,including 0...but still more conditions need to be checked for 0,which I did not check...and graph now clearly shows only 4 points..thanks eliassaab for pointing out....