f(x) = 4 + 4x^2 − x^4

find inflection points.

Question

f(x) = 4 + 4x^2 − x^4

find inflection points.

anonymous · Answer

imstuck · Answer

find the second derivative of this, set it equal to 0 and these will be your points.

imstuck · Answer

rewrite in descending order to make it a little more digestible!!!  lol

anonymous · Answer

$$12x^2-8$$=0

anonymous · Answer

$$x=\sqrt{2/3}$$

imstuck · Answer

The second derivative is$$f''(x)=-12x ^{2}+8$$set it equal to 0:$$0=-12x ^{2}+8$$or better yet:$$0=12x ^{2}-8$$

anonymous · Answer

then to get y coordinates i plug that into f(x)
and I get 6, but its not the right answer

imstuck · Answer

its not $$\sqrt{\frac{ 2 }{ 3 }}$$it's$$\sqrt{\frac{ 3 }{ 2 }}$$

anonymous · Answer

why and how do you know which number to bring over first?

imstuck · Answer

like this:

imstuck · Answer

wait you're right...I'm wrong!  It is your answer, so let's see what's up!

anonymous · Answer

its 56 over 9
stupid mistake

imstuck · Answer

$$f''(\sqrt{\frac{ 2 }{ 3 }})=12(\sqrt{\frac{ 2 }{ 3 }})^{2}-8$$$$f''=\frac{ 24 }{ 3 }-8$$That equal 0.  Did you get 0?

imstuck · Answer

wait, what is 56/9?

imstuck · Answer

I get 0 for the inflection point.

anonymous · Answer

how

anonymous · Answer

i gotta leave for class in 8 mins, thanks buddy i'll be on here later asking questions.

imstuck · Answer

because$$f''(\sqrt{\frac{ 2 }{ 3 }})=12(\sqrt{\frac{ 2 }{ 3 }})^{2}-8$$and$$f''=12(\frac{ 2 }{ 3 })-8$$and$$f''=\frac{ 24 }{  }-8=0$$

imstuck · Answer

thats over 3.  it = 0,  test -1 in f'' and 1 in f'' annd you get that the function is increasing to the inflection point

imstuck · Answer

$$f''=\frac{ 24 }{ 3 }-8$$is$$f''=8-8$$try -1 and +1 in your f'' equation and see what the results are!

imstuck · Answer

I bet it looks like this:|dw:1405364554771:dw|it's increasing on the negative side of 0 and increasing on the positive side of 0

imstuck · Answer

TY for the medal, even if you are gone from here!