Use the formula below to find the instantaneous rate of change of the function at the givenx-value.

f(x) =4x²+2xatx=9

• Average and Instantaneous Rate of Change
• Theaveragerate of change of a functionfbetweenxandx+h
• is
• f(x+h)f(x)
• h
• .
• (Difference quotient gives theaveragerate of change.)
• Theinstantaneousrate of change of a functionfat the numberxis
• lim
• h0
• f(x+h)f(x)
• h
• (Taking the limit makes itinstantaneous.)