label Calculus
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1. For the function f(x)=x^2-4x:

a.Determine the average rate of change from x=1 to x=4

b. Determine the instantaneous rate of change at x=1.

Oct 16th, 2017

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

$f(4)=4^2-4\times4=16-16=0\\$

$f(1)=1^2-4\times1=1-4=-3\\$

Average rate of change from x=1 to x=4

$\\ =\frac{f(4)-f(1)}{4-1}\\ \\ =\frac{0-(-3)}{3}\\ \\ =\frac{0+3}{3}\\ \\ =\frac{3}{3}\\ \\ =1$

To find the instantaneous rate of change differentiate f(x) w.r.t. x

$\\ f'(x)=2x-4$

Now substitute x = 1

$\\ f'(1)=2\times1-4=2-4=-2$

Average rate of change = 1

Instantaneous rate of change = -2

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Jul 19th, 2015

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Oct 16th, 2017
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Oct 16th, 2017
Oct 17th, 2017
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