Question

what is the diference when dy/dx = 0 and d 2 y/dx 2 = 0

Answer 1

hey friend.

=) dy/dx is the 1st derivative of any function..

=) dy/dx represent the slope of tangent at any point

But d^2y/dx^2 is second derivative.

=)it represent curvature of any curve.

=) curvature in sense :-

where curve will turn I.e upward or downward.

example :--

let a function :- y = x^2

so dy/dx = 2x

=) slope if tangent at any point is " 2x "

and,..

=) d^2y/dx^2 = 2

but ,. 2 > 0 (positive ) so curve is open upward ....

if second derivative comes to be negative (<0 ) then curve open downward.

this is the geometrical meaning of second derivative.

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hope it will help u