Question

Find an equation of the tangent line to the curve at the point (1,1/e). y=x^4*e^-x

Answer 1

We will use y-y1=m(x-x1), where m= f '(x)= 4x^3e^-x - x^4e^-x, f ' (1) =3e^-1
f  (1) =4e^-1
so the equation of tangent line tothe curve at the point (1,1/e) is 
y= 3e^-1(x-1) + 4e^-1, or y= 3e^-1(x)) + e^-1,