Please show supporting analysisthank you Write response on scratch paper.The accompanying figure shows a portion of the graph of a function that is twice-differentiable at all x except at x = p. At each of the labeled points, classify y' and y"as positive, negative, zero, or undefined.X = P

Given: the given accompanying figure shows a portion of the graph that is twice differentiable at all x except x=p. and the figure is given below: To classify: y' and y" as positive, negative zero or undefined. Point a The point a is a cusp for which the limitlimh→0fa+h-fah DOES NOT EXIST. Therefore, for point a, y'=undefined, y"=undefined {given}Point b The slope at point b is zero and the point is a LOCAL MINIMUM. From second derivative test, local minima exists when y'' > 0. Therefore, for point b, y'=zero, y"=positive Point c The slope of the curve at point c is POSITIVE and around point c the concavity of the curve changes from CONCAVE UPWARDS to CONCAVE DOWNWARDS. Therefore, point c is the POINT OF INFLECTION. for point c, y'=positive, y"=zero Point d The slope at point d is ZERO. Around point d the concavity of the curve changes from CONCAVE DOWNWARDS to CONCAVE UPWARDS Therefore, point d is the POINT OF INFLECTION. for point d, y'=zero, y"=zero Point e At the point e the concavity of the curve is CONCAVE DOWNWARDS and slope is POSITIVE. From second derivative test, the curve is CONCAVE DOWNWARDS when y''<0 for point e, y'=positive, y"=negative Point f At the point f slope is ZERO and the point is a LOCAL MAXIMA. From second derivative test, the point is a LOCAL MAXIMA if y''<0. for point f, y'=zero, y"=negative Point g At the point g slope is NEGATIVE and the concavity of the curve changes from CONCAVE DOWNWARDS to CONCAVE UPWARDS. for point g, y'=negative, y"=zero