Menu Close

minimum-of-function-y-x-2-e-2x-is-




Question Number 78046 by jagoll last updated on 13/Jan/20
minimum of   function y = (√(x^2 +e^(2x) ))  is
minimumoffunctiony=x2+e2xis
Answered by john santu last updated on 13/Jan/20
y′ = ((2x+2e^(2x) )/(2(√(x^2 +e^(2x) )))) = 0  e^(2x)  = − x , x<0   1 = −xe^(−2x)  ⇒ use Lambert W  function
y=2x+2e2x2x2+e2x=0e2x=x,x<01=xe2xuseLambertWfunction
Commented by john santu last updated on 13/Jan/20
2 =−2xe^(−2x)  ⇒W(2)= W(−2xe^(−2x) )  W(2)= −2x ⇒ x=−((W(2))/2)
2=2xe2xW(2)=W(2xe2x)W(2)=2xx=W(2)2

Leave a Reply

Your email address will not be published. Required fields are marked *