Question

y=1/x^2 find the concavity, where its increasing and decreasing, the point of inflection, and graph it.

Answer 1

If

\[\Large f(x) = \frac{1}{x^2}\]

then what is \(\Large f'(x)\) equal to?

Answer 2

what do you mean

Answer 3

are you able to find the derivative?

Answer 4

hehe sounds like a nope

Answer 5

\[\lim_{h \rightarrow 0}\frac{ \frac{ 1 }{ (x+h) ^{2} }-\frac{ 1 }{ x ^{2} } }{ h }\]

Answer 6

~ find f''(x).

~ set f''(x)=0 and solve for x

~ this will give you the x. so find the points on the function of these X-s.
{ call inflections x=a b c then the points of inflections are (a,f(a)) , (b,f(b)) , (c,f(c)). }

Answer 7

to differentiate, re-write it as x^-2, and use the power rule.

Answer 8

to find increasing and decreasing use f ' (x)=0
to find concavity and inflection point use f '' (x)=0

Answer 9

Hope the attached plot from Mathematica 9 will help.

Answer 10

lol, failed to load... :P