Stuck at solving equation Hi. I can't find an answer to the equation $\displaystyle e^x+x3=0$. I'm not sure how to solve it. 
Just apply Newton's method. This gives a solution $x = .7921...$. Since the expression is monotone increasing, this must be a unique solution. 
I have already done that in the second question where they tell you to use Newton´s method. But the first question is: Show that we can find the value of a, solving the equation e^x+x3=0. 
The task is: The tangent to the curve $\displaystyle y=e^{2x} $ in $\displaystyle x=2 $ cuts the curve $\displaystyle y=e^x $ in a point where x=a. 
The equation has no analytic solution, only numerical. 
Ok, but how to I proceed to solve it numerical? 
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$f(x) = e^x + x  3.$ Is f(x) continuous? What is the sign of f(0)? What is the sign of f(1)? What does all that imply about the existence of a such that f(a) = 0? 
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