F.4 app. of differentiation

1)
Find the equation of the tangent to the curve y=e^(-1/x) at the point
(1,1/e) .
ans: x-ey=0

2) The equation of a curvwe C is given by y=x/lnx
a)find a point on the curve C such that the slope of the tangent to C is -2.
b)find the equation of the tangent to C which is parallel to the line 2x+y-10=0


3) Show each of the following function is increasing for all real values of x.

a)f(x)=x^3+3x^2+4x+1
b) f(x)=e^x/e^(-x)+2

4) It is given that f(x)= 3x+1/x^2+2x+3.Find the ranges of values of x such that
a) f(x) is increasing
b)f(x) is decreasing


pls show clear steps.thz!