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poizon [28]
2 years ago
14

Find the average rate of change of the function f(x) equals -1X^2-4x-3 from x=-1 to x=5

Mathematics
1 answer:
vladimir2022 [97]2 years ago
7 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}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=-x^2-4x-3 \qquad \begin{cases} x_1=-1\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(-1)}{5-(-1)} \\\\\\ \cfrac{[-(5)^2-4(5)-3]~~-~~[-(-1)^2-4(-1)-3]}{5+1} \\\\\\ \cfrac{[-25-20-3]-[-1+4-3]}{6}\implies \cfrac{[-48]-[0]}{6}\implies \cfrac{-48}{6}\implies -8

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Similar to this train of thought, the first equation is formulated by doing exactly that. 'q' represents an unknown number of quarters, and 'd' an unknown number of dimes. We use 25q and 10d, because, well, we're multiplying their value by the number of coins. They're equivalent to 425 because the 20 unknown coins make $4.25 (I converted it to cents to get rid of the pesky decimals, but if you want to keep it as dollars that works too).

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