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Re: Mathematica Question

• To: mathgroup at smc.vnet.net
• Subject: [mg66381] Re: Mathematica Question
• From: "Scout" <Scout at nodomain.com>
• Date: Thu, 11 May 2006 02:15:20 -0400 (EDT)
• References: <e3shhl$m39$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Bharat Bhole" <bbhole at gmail.com>
news:e3shhl$m39$1 at smc.vnet.net...
> Hello:
>
> Is there a way in Mathematica to check whether an algebraic expression is
> positive or negative, and a way to specify conditions on the variables in
> the expression? For example, is there a way to check whether x^2 is 
> positive
> for any real x? I want to check this for a complicated
> expression...basically the sign of the second derivative of a function.
>
> Thank you very much for your help.
>
> Bharat.
>
>
Hi Bharat,
I suppose that you need the Simplify[] command.

In[1]:= Simplify[x^2 >= 0, x \[Element] Reals]
Out[1]= True

In[2]:= f[x_] := x^3;
In[3]:= Simplify[{f[x] > 0, f''[x] > 0}, x > 0]
Out[3]= {True, True}
In[4]:= Simplify[{f[x] > 0, f''[x] > 0}, x < 0]
Out[4]= {False, False}

Hope this helps,
    ~Scout~