A point on the curve y=(x−3)2, where the tangent is parallel to the chord joining the points (3,0) and (4,1)

we have, y=(x−3)2, which is polynomial function. So it is continuous and differentiable.  Thus conditions of mean value theorem are satisfied.  Hence, there exists at least one c∈3,4  such that,f′(c)=f(4)−f(3)4−3⇒2(c−3)=1−01⇒c−3=12⇒c=72∈(3,4)⇒x=72, where tangent is parallel to the chord joining points (3,0) and (4,1) For x=72,y=72−32=122=14 So, 72,14 is the point on the curve, where tangent drawn is parallel to the chord joining the  points (3,0) and (4,1)