# Inequalities

• Nov 13th 2012, 08:08 AM
Petrus
Inequalities
What is the smallest value of a for which the inequality https://webwork.math.su.se/webwork2_...5445c9ff01.png is observed for x> 0?
what i thought is that i put x = 1 and solve it but did not work well :(
• Nov 13th 2012, 08:26 AM
ebaines
Re: Inequalities
You can rearrange to $2 \ln x - 3x^2 - 6x \le a$, then find the max value for the left hand side in the interval x>0. That max value is the value for a.
• Nov 13th 2012, 08:29 AM
Petrus
Re: Inequalities
Quote:

Originally Posted by ebaines
You can rearrange to $2 \ln x - 3x^2 - 6x \le a$, then find the max value for the left hand side in the interval x>0. That max value is the value for a.

hmmm i still dont get any progress :S
• Nov 13th 2012, 08:38 AM
ebaines
Re: Inequalities
Quote:

Originally Posted by Petrus
hmmm i still dont get any progress :S

Do you know how to find the max value of a function? Hint - start by finding where the derivative = 0....
• Nov 13th 2012, 08:44 AM
Petrus
Re: Inequalities
Quote:

Originally Posted by ebaines
Do you know how to find the max value of a function? Hint - start by finding where the derivative = 0....

ok i got these
x=1/6(sqrt(21)-3)
x=1/6(-3-sqrt(21))
is this correct? ajnd what shall i do next
• Nov 13th 2012, 09:24 AM
ebaines
Re: Inequalities
Quote:

Originally Posted by Petrus
is this correct?

Yes, those are the values of x where the derivative is 0. But remember you only need worry about x>0.

Quote:

Originally Posted by Petrus
what shall i do next

Next step - what is the value of $2 lnx - 3x^2 -6x$ at this value of x? That's what 'a' is equal to.