A function is given. Determine the average rate of change of the function betwee

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A function is given. Determine the average rate of change of the function between the given values of the variable.

f(x) = 4x2;    x = 2, x = 2 + h

Jun 28th, 2015

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$f(x)=4x^2\\$

$f(2)=4\times2^2=4\times4=16\\$

$\\ f(2+h)=4(2+h)^2\\ \\ f(2+h)=4(2^2+2\times2\times h+h^2)\\ \\ f(2+h)=4(4+4h+h^2)\\ \\ f(2+h)=16+16h+4h^2\\$

Average rate of change

$\\ =\frac{f(2+h)-f(2)}{2+h-2}\\ \\ =\frac{16+16h+4h^2-16}{h}\\ \\ =\frac{16h+4h^2}{h}\\ \\ =\frac{h(16+4h)}{h}\\ \\ =4h+16$

ANSWER:  4h + 16

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