Having trouble finding the solution to e x − 3 e − x − 4 x = 0. The answer is roughly 2.2 but am not sure how to get there?

Question

Having trouble finding the solution to       e    x    −  3      e          −      x        −  4  x  =  0. The answer is roughly   2.2 but am not sure how to get there?

Quinn Alvarez · Accepted Answer

Let   f  (  x  )  =      e    x    +  3      e          −      x        −  4  xFind   a  ,  b such that   a  &amp;lt;  b and either   f  (  a  )  &amp;lt;  0  &amp;lt;  f  (  b  ) or   f  (  a  )  &amp;gt;  0  &amp;gt;  f  (  b  ) (i.e. find two points such that the function changes sign between them, meaning there is a solution somewhere in that interval - this only works because   f is a continuous function).Take   c  =      1    2    (  a  +  b  ). If   f  (  c  )  =  0 then 𝑐 is the desired zero, and you can stop. Or, if   f  (  c  ) is smaller than the error you&#039;re willing to accept, then it&#039;s your approximation and you can stop.Find the sign of   f  (  c  ). If   f  (  a  ) and   f  (  c  ) have the same sign, set   a  :=  c, otherwise set   b  :=  c (i.e. pick a new   a and   b such that you still know that the zero is between them).Go back to step   2 with your new   a and   b.

Having trouble finding the solution to e:x−3e:(−x)−4x=0. The answer is roughly 2.2 but am not sure how to get there?

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