Ordinate of the point on the curve y=x^x where tangent drawn to the curve is parallel to x axis is - Maths - Application of Derivatives

Question

Ordinate of the point on the curve y=x^x where tangent drawn to the
curve is parallel to x axis is a)e^(1/e) b) 1/e c) e^(-1/e) d)
1/(e^e)

Brijendra Pal · Accepted Answer

Dear Student, y = xxTaking ln, lny = xlnxdifferentiating both side, 1ydydx= 1+lnxdydx= 1+lnxxxNow if slop is parallel to x-axis then dydx=0  1+lnxxx= 0  1+lnx=0lnx = -1x = e-1= 1eRegards

Ordinate of the point on the curve y=x^x where tangent drawn to the curve is parallel to x axis is a)e^(1/e) b) 1/e c) e^(-1/e) d) 1/(e^e)