f(x) = 3x^2; x = 4, x = 4 + h

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Determine the average rate of change of the function. 

Sep 11th, 2015

Thank you for the opportunity to help you with your question!

f(x) = 3x^2; x = 4, x = 4 + h

F(4) = 3(4)^2

f(4)=3(16)

f(4)=48


f(4+h)=3(4+h)^2

f(4+h)=3 x (4+h)(4+h)
f(4+h)=3 x (16+8h +h^2 )
f(+h)=48+24h +3h^2

=(48- 48+24h +3h^2)/(4-4+h)
=(3h^2 +24h)/h

Simplify the numerator to get
3h(h+8)/h

Dividing through by h gives 3(h+8)
the answer is 3h +8

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 11th, 2015

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