The expression for h 0 is caled the difference quotient Fi

The expression )-) for h # 0 is caled the difference quotient Find and singify the dferencequotent for the following f reson 8x2+5x7 The difference quotient is (Simplity your answer

Solution

1) Difference quotient

f(x) = 8x^2 +5x +7

f(x+h) = 8(x+h)^2 +5(x+h) +7

f(x+h) -f(x) = { 8(x+h)^2 +5(x+h) +7 } - (8x^2 +5x +7)

= 8h^2+ 16xh+5h

{ f(x+h) -f(x) }/h = (8h^2+ 16xh+5h )/h = 8h +16x+5