How do you find the average rate of change of $f (x) = x^{3} - 3 x + 5$ $f(x)=x^3-3x+5$ over [5,7]?

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Answer 1 · 2015-10-19T10:47:35

Just plug the values $5 and 7$ $5and7$ in the function and see what $y$ $y$ does.

$f (7) = 7^{3} - 3 \cdot 7 + 5 = 327$ $f(7)=7^3-3*7+5=327$
$f (5) = 5^{3} - 3 \cdot 5 + 5 = 115$ $f(5)=5^3-3*5+5=115$

Then you divide difference in $f (x)$ $f(x)$ by difference in $x$ $x$ :

$(Deltaf(x))/(Deltax)=(327-115)/(7-5)=212/2=106$

How do you find the average rate of change of f(x)=x^3-3x+5f(x)=x3−3x+5f(x)=x^3-3x+5 over [5,7]?