Question

f(x)=x^1/x maxima and minima

Answer 1

Answer:

minima= e^1/e

Step-by-step explanation:

let y=x^1/x

lny=ln(x^1/x)

lny=1/x*lnx

differentiating wrt x

1/y dy/dx=-1/x²*lnx+1/x²

dy/dx= y(1-lnx)/x²

dy/dx=x^1/x(1-lnx)/x²

For maxima or minima, dy/dx=0

(x^1/x)*(1-lnx)/x²=0

Since x^1/x can never be 0,=> 1-lnx=0

lnx=1

x=e

Now, minima= e^1/e