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QuestionFind the average rate of change of f(x)f(x) from x1=−9x_{1}=-9 to x2=−1x_{2}=-1, rounded to the nearest hundred. f(x)=−8x+6 f(x)=\sqrt{-8 x+6}

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=−8x+6f(x)=\sqrt{-8 x+6} . The initial point is x1=−9x_{1}=-9
3. The final point is x=−1x_{}=-1
4. We are asked to find the average rate of change of the function from x1x_{1} to xx_{}

STEP 2

The average rate of change of a function f(x)f(x) from x1x_{1} to x2x_{2} is given by the formulaAverage rate of change=f(x2)−f(x1)x2−x1\text{Average rate of change} = \frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}

STEP 3

First, we need to find the value of the function at x1=−9x_{1}=-9. Substitute x1=−9x_{1}=-9 into the function f(x)f(x).
f(x1)=f(−9)=−8(−9)+6f(x_{1}) = f(-9) = \sqrt{-8(-9)+6}

STEP 4

Calculate the value of f(x1)f(x_{1}).
f(x1)=72+6=78f(x_{1}) = \sqrt{72 +6} = \sqrt{78}

STEP 5

Next, we need to find the value of the function at x2=−1x_{2}=-1. Substitute x2=−1x_{2}=-1 into the function f(x)f(x).
f(x2)=f(−1)=−8(−1)+f(x_{2}) = f(-1) = \sqrt{-8(-1)+}

STEP 6

Calculate the value of f(x2)f(x_{2}).
f(x2)=8+6=14f(x_{2}) = \sqrt{8 +6} = \sqrt{14}

STEP 7

Now that we have the values of f(x1)f(x_{1}) and f(x2)f(x_{2}), we can substitute these into the formula for the average rate of change.
Average rate of change=14−78−1−(−9)\text{Average rate of change} = \frac{\sqrt{14} - \sqrt{78}}{-1 - (-9)}

STEP 8

implify the denominator.
Average rate of change=14−788\text{Average rate of change} = \frac{\sqrt{14} - \sqrt{78}}{8}

STEP 9

Calculate the average rate of change. Round your answer to the nearest hundredth.
The average rate of change of f(x)f(x) from x=−9x_{}=-9 to x2=−x_{2}=- is approximately −.00-.00.

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