Question - Need help! (1 Viewer)

[Dr. Zoidberg]

Find the values of p for which x²-x+3p-2>0 for all x.

Thanks!

^<o>
</o>

 

[vds700]

Find the values of p for which x²-x+3p-2>0 for all x.

Thanks!

^<o>
</o>

delta = b^2 - 4ac
=1 - 4(1)(3p - 2)
=1 - 12p + 8
=9 - 12p

for f(x) > 0, it must be above the x-axis, (not below as the coefficient of x^2 is positive), so delta <0
9 - 12p < 0
9 < 12p
12p > 9
p > 3/4

 

[Dr. Zoidberg]

Lifesaver!

Thanks!

 

[conics2008]

Find the values of p for which x2-x+3p-2>0 for all x.

Step one: find dy/dx = 2x -1
step two: equate dy/dx=0 hence x=1/2
step three: find if its minimum or max.. using f''(x) >0 minimum
step four: sub x=1/2 into f(x)

f(1/2)= 1/4-1/2+3p-2>0 hence p>3/4

This is more advanced method, just incase you dont get a quadratic equation next time, use this method.

 

[tommykins]

回复: Re: Question - Need help!

Find the values of p for which x2-x+3p-2>0 for all x.

Step one: find dy/dx = 2x -1
step two: equate dy/dx=0 hence x=1/2
step three: find if its minimum or max.. using f''(x) >0 minimum
step four: sub x=1/2 into f(x)

f(1/2)= 1/4-1/2+3p-2>0 hence p>3/4

This is more advanced method, just incase you dont get a quadratic equation next time, use this method.

Also note that this method wouldn't work on odd functions.

 

[Dr. Zoidberg]

Thanks for the extra tips conics2008 and tommykins

 

[lolokay]

Re: 回复: Re: Question - Need help!

Also note that this method wouldn't work on odd functions.

eh you can't really have an odd function that is greater than a certain number for all values of x anyway, can you?

 

[melanieeeee.]

Re: 回复: Re: Question - Need help!

omgsh its dr. zoidberg. i am your biggest fan. woop woop woop woop woooooop...

 

[Dr. Zoidberg]

Re: 回复: Re: Question - Need help!

omgsh its dr. zoidberg. i am your biggest fan. woop woop woop woop woooooop...

HOORAY for me! HOORAY for ZOIDBERG! Zoidberg has a fan

Woop woop woop woop woop woop woop woop

P.S. Zoidberg ftw

 

[tommykins]

Re: 回复: Re: Question - Need help!

eh you can't really have an odd function that is greater than a certain number for all values of x anyway, can you?

Exactly. All odd functions must have a real root.