Algebra Pre-Algebra and Basic Algebra Math Forum

 April 14th, 2014, 09:54 AM #1 Newbie   Joined: Apr 2014 From: The Netherlands Posts: 7 Thanks: 2 Line intersections Edit: Oops! This is in the wrong section, maybe it better fits in pre-calc/calc. I'll just walk through the question as it is asked in the book I'm studying. Excuse me for grammar errors. Suppose we have the following function: a) Calculate the extreme value of f(x) and give the range of f(x) So, we simply need to calculate f'(x) and set it to zero. Because I did answer a) correctly, I'll simply just get continue with posting f'(x) instead of deriving it step by step. Now we need to set it to zero. Which will yield: Putting these values in the original equation will result in the extreme values: (minimum) and (maximum). The range of f(x) will thus be b) Calculate (algebraically) for which a the equation f(x) = ax has exactly one unique solution. So, from this point on I have absolutely no idea what to do. Can anyone help me out? c) Calculate (algebraically) for which p the equation f(x) = 2/3x + p has three solutions. I thought that if I could get some help on b I could try and solve b and c in this topic :^). Last edited by jyrdo; April 14th, 2014 at 10:01 AM. Reason: Wrong section April 14th, 2014, 11:47 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,664 Thanks: 2644 Math Focus: Mainly analysis and algebra You need to find where $f(x) = ax$. That is the same as finding where $$g(x) = f(x) - ax = 0$$ So, try solving that for $x$, and see what value of $a$ gives a single (possibly repeated) solution in the real numbers. April 14th, 2014, 12:13 PM   #3
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 Originally Posted by v8archie You need to find where $f(x) = ax$. That is the same as finding where $$g(x) = f(x) - ax = 0$$ So, try solving that for $x$, and see what value of $a$ gives a single (possibly repeated) solution in the real numbers.

I get that I have to find where $f(x) = ax$, but I don't think I'll find it the way I'm trying right now. April 15th, 2014, 03:04 AM #4 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,948 Thanks: 1139 Math Focus: Elementary mathematics and beyond $\displaystyle \frac{6x}{x^2+5}=ax$ $\displaystyle 6=ax^2+5a$ $\displaystyle ax^2=6-5a=0\Rightarrow a=\frac65$ Tags intersections, line Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Prold Real Analysis 2 April 21st, 2013 12:51 PM Math4dummy Algebra 2 February 6th, 2012 08:10 AM soulrain Algebra 2 January 6th, 2012 10:21 AM Gerd Isenberg Applied Math 10 October 1st, 2009 10:46 PM organismal Algebra 1 September 9th, 2009 09:06 PM

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