f ( x ) is a continuous function on R and y = f ( x ) is a curve. If ( , ) is a point such that =f( ) and p +m +n=0( p 0, ~m 0) , then which one of the following is True?

Step-by-step solution

Since f(x) is a curve contains ( , ) and p + m + n =0 ... (i) So, curve intersect px + my + n =0 Let equation of curve y=f(x)=a x^2+b x+c aligned & =a ^2+b +c putting in (i), we get & P +m a ^2+m b +c+n=0 ... (ii) & f(x)=a x^2+b x+c f^ (x)=2 a x+b aligned Now, p+m f^ ( )=p+m(2 a +b) from (i) = c + n - ma 0