Sketch the graph of a smooth function ?j? and label a point ?P?(?a,? (?f?(?a?))on the curve. Draw the line that represents the linear approximation to ?f? at ?P.

SOLUTION STEP 1 A function is said to be smooth if it has continuous derivatives upto some desired order over some domain.Therefore a function can be said to be smooth over a restricted interval such as (a,b) or [a,b] STEP 2 The graph of a smooth function j is