determine concavity

[fran1942]

Hello, I need to determine concavity of the function: "cosx / x" at pi.

My first step is to derive to:
{-xsinx + cosx} / x^2

then I derive again to:

{(x^2+2)cosx} / x^3

then I plug in piug in pi which gives -0.38 which means concave down.
However looking at the graph of the original function" cosx / x, I see that at position pi, the graph is actually concave up.
Can anyone please see where I am going wrong ?

Thanks kindly

 

[Deleted member 4993]

Hello, I need to determine concavity of the function: "cosx / x" at pi.

My first step is to derive to:
{-xsinx + cosx} / x^2............... that should be {-xsinx - cosx} / x^2

then I derive again to:

{(x^2+2)cosx} / x^3

then I plug in piug in pi which gives -0.38 which means concave down.
However looking at the graph of the original function" cosx / x, I see that at position pi, the graph is actually concave up.
Can anyone please see where I am going wrong ?

Thanks kindly

.

 

[renegade05]

Quotient rule states:

\(\displaystyle f'(x)=\frac{g'(x)h(x)-g(x)h'(x)}{[h(x)]^2}\)

...ugh nevermind latex down....

Here is the rule in plain text:

f'(x)=(g'(x)h(x)-g(x)h'(x))/([h(x)]^2)