Calculus families of functions

Question

find the coordinates of critical point y = xe^-bx

Answer 1

Hi,

y = xe^-bx

is your question y = x e^-bx ???

if yes, take a derivative of function

y' = 1 * e^-bx + -be^-bx * x ( follow product rule)

y' = e^-bx ( 1 -bx )

y' = 0 -----> e^-bx ( 1 -bx ) = 0 you see only inside of perenties must be zero

1 -bx = 0 ------> x = 1/b then replace to the given function and find the y of critical point

y = x e^-bx = 1/b ( e^-b(1/b)) = 1/b * e-1 = 1/be critical point is ( 1/b , 1/be)

^{I hope it is useful,}

^Minoo