Calculate the average rate of change for the function f(x)=x^4+3x^3-5x^2+2x-2, from x=-1 to x=1

1 answer:

6 0

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\
f(x)= x^4+3x^3-5x^2+2x-2 \qquad 
\begin{cases}
x_1=-1\\
x_2=1
\end{cases}\implies \cfrac{f(1)-f(-1)}{1-(-1)}
\\\\\\
\cfrac{[1+3-5+2-2]~~-~~[1-3-5-2-2]}{1+1}\implies \cfrac{[-1]~~-~~[-11]}{2}
\\\\\\
\cfrac{-1+11}{2}\implies \cfrac{10}{2}\implies 5$

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