My Math Forum Assignment

 Algebra Pre-Algebra and Basic Algebra Math Forum

November 17th, 2012, 06:07 AM   #1
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Assignment

Hey guys I have problems finding the x value shown in the attached file. The text isn't in English, but you only have to look at the graphs in order to understand how to solve the problem. A(x) describes the area of the triangle, while p is the corner of the triangle on the function f(x).

I think I know how to solve it, but I'm not sure:

f'(x)=f(x) and find x, then I will find the slope for P=-0,693

then I put the differentiated equation to be equal to the slope, and isolate x: f'(x)=-0.693 -> x=0,65

Is it correct?

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 November 20th, 2012, 02:46 PM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Assignment [color=#000000]a. $f(x)=-\frac{e^{x}+e^{-x}}{2}+2=-cosh(x)+2$ in order to find the coordinates of B you have to solve the equation $f(x)=0\Leftrightarrow cosh(x)=2\Leftrightarrow x=\textrm{arccosh}(2)$ and so $B(\textrm{arccosh}(2),0)$. b. $A(x)=\frac{1}{2}\cdot x\cdot f(x)=\frac{1}{2}x\left(-\frac{e^{x}+e^{-x}}{2}+2\right)=-\frac{1}{2}xe^{x}-\frac{1}{2}xe^{-x}+x$[/color]

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