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`"Let "x=3 and x+Deltax=3.01` <br> ` rArr Deltax= 0.01` <br> `"At "x=3, y=f(3)=3^(2)+3(3)+1=19` <br> `"Now " y=x^(2)+3x+1` <br> ` rArr (dy)/(dx) = f'(x)=2x+3` <br> `"At "3,` <br> ` (dy)/(dx)=f'(x)=2(3)+3=9` <br> `:. Deltay=(dy)/(dx).Deltax=9(0.01)=0.09` <br> `and y+Deltay=19+0.09` <br> ` rArr f(3.01) = 19.09`.**Introduction: average rate and instantaneous rate**

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