`h(p) = (p - 1)/(p^2 + 4)` Find the critical numbers of the function

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Given: `h(p)=(p-1)/(p^2+4)`

Find the critical value(s) by setting the first derivative equal to zero and solving for the x value(s). Find the derivative by using the quotient rule.

`h'(p)=[(p^2+4)(1)-[(p-1)(2p)]]/[p^2+4]^2=0`

`h'(p)=p^2+4-(2p^2-2p)=0`

`h'(p)=p^2+4-2p^2+2p=0`

`h'(p)=-p^2+2p+4=0`

`h'(p)=p^2-2p-4=0`

`p^2-2p-4=0`

`p^2-2p+1=4+1`

`(p-1)^2=5`

`p-1=+-sqrt(5)`

` ` `p=1+-sqrt(5)`

The critical values are `x=1+sqrt(5),x=1-sqrt(5).`

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Given: `h(p)=(p-1)/(p^2+4)`

Find the critical value(s) by setting the first derivative equal to zero and solving for the x value(s). Find the derivative by using the quotient rule.

`h'(p)=[(p^2+4)(1)-[(p-1)(2p)]]/[p^2+4]^2=0`

`h'(p)=p^2+4-(2p^2-2p)=0`

`h'(p)=p^2+4-2p^2+2p=0`

`h'(p)=-p^2+2p+4=0`

`h'(p)=p^2-2p-4=0`

`p^2-2p-4=0`

`p^2-2p+1=4+1`

`(p-1)^2=5`

`p-1=+-sqrt(5)`

` ` `p=1+-sqrt(5)`

The critical values are `x=1+sqrt(5),x=1-sqrt(5).`

``

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