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Finding the highest factor by Differentiation method

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by iikarthik » Tue Jul 27, 2010 11:51 am
Hi All,

I remember having read the use of differentiation to find the highest value of a given quadraric equation.

But am not able to get it right.
can someone pls explain what went wrong.

the equation is x^2-6x-27=0
by Diff with respect to X, we get 2x-6=0.hence x=3

but by factorising, we get the values of X as 9,-3.

Thanks
karthik
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by Brent@GMATPrepNow » Tue Jul 27, 2010 12:16 pm
Hi Karthik,

You are answering 2 different questions.

You would use differentiation to find the maximum or minimum value of an expresson such as x^2-6x-27
However, if you wish to solve the equation x^2-6x-27 = 0, then you would factor --> (x-9)(x+3)=0 --> x=9, -3

Cheers,
Brent

PS: Differentiation is not required on the GMAT :-)
PPS: the expression x^2-6x-27 has no maximum value, but its minimum value occurs at x=3


iikarthik wrote:Hi All,

I remember having read the use of differentiation to find the highest value of a given quadraric equation.

But am not able to get it right.
can someone pls explain what went wrong.

the equation is x^2-6x-27=0
by Diff with respect to X, we get 2x-6=0.hence x=3

but by factorising, we get the values of X as 9,-3.

Thanks
karthik
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by gmatmachoman » Wed Jul 28, 2010 2:54 am
Brent Hanneson wrote:Hi Karthik,

You are answering 2 different questions.

You would use differentiation to find the maximum or minimum value of an expresson such as x^2-6x-27
However, if you wish to solve the equation x^2-6x-27 = 0, then you would factor --> (x-9)(x+3)=0 --> x=9, -3

Cheers,
Brent

PS: Differentiation is not required on the GMAT :-)
PPS: the expression x^2-6x-27 has no maximum value, but its minimum value occurs at x=3


iikarthik wrote:Hi All,

I remember having read the use of differentiation to find the highest value of a given quadraric equation.

But am not able to get it right.
can someone pls explain what went wrong.

the equation is x^2-6x-27=0
by Diff with respect to X, we get 2x-6=0.hence x=3

but by factorising, we get the values of X as 9,-3.

Thanks
karthik
D = b^2 -4ac
= 6^2 -4 *1*(-27)
>0
Minimum value when D >0 and Maximum value when D<0

So for the above expression only Minimum can be found out as D is >0

Hope I am correct..
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