Horizontal tangent line? For what value(s?? is the line tangent to the curve y = x 6?x horizontal?

Solution Step 1: Given y = x 6 x dy To find the values of x at which y has horizontal tangent first we find dx To find dy we need following formulae dx d dv du dx(uv) = udx + v dx Step 2 dy d dx= dx (x 6 x) =x d ( 6 x) + 6 x d (x) dx dx 1 d d 1 =x 2 6x dx(6 x) + 6 x(1) ( dx x = 2x ) =x 1 + 6 x 2 6x = x+2(6x) 6x 123x = 6x