My Math Forum (http://mymathforum.com/math-forums.php)
-   Algebra (http://mymathforum.com/algebra/)
-   -   Assignment (http://mymathforum.com/algebra/31830-assignment.html)

 LMW November 17th, 2012 06:07 AM

Assignment

1 Attachment(s)
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?

[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]