The slope of the secant line through (a,f(a)) and (a+h, f(a+h)) is given by the difference quotient
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Expression 8: "m" equals StartFraction, left parenthesis, "f" left parenthesis, "a" plus "h" , right parenthesis minus "f" left parenthesis, "a" , right parenthesis , right parenthesis Over "h" , EndFractionm=fa+h−fah
equals=
negative 16−16
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The derivative at x=a is the limit of the difference quotient as h tends to 0
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Expression 10: "f" prime left parenthesis, "a" , right parenthesisf′a