Question

What is the average rate of change of f(x) = -10x³ + 7x² - 5x - 4 from x1 =-0.7 to x2=4.2? Please write your answer rounded to the nearest hundredth

Answer 1

Answer:

The average rate of change = -132.40

Step-by-step explanation:

The given function is:

f(x) = -10x³ + 7x² - 5x - 4

At x₁ = -0.7

f(-0.7) = -10(-0.7)³ + 7(-0.7)² - 5(-0.7) - 4

f(-0.7) = 6.36

At x₂ = 4.2

f(4.2) = -10(4.2)³ + 7(4.2)² - 5(4.2) - 4

f(4.2) = -642.4

The average rate of change of f(x) is calculated as:

`\begin{gathered} (\triangle f(x))/(\triangle x)=(f(x_2)-f(x_1))/(x_2-x_1) \\ (△f(x))/(△x)=\frac{f(4.2)-f(-0.7)}{4.2-(-0.7)_{}} \\ (△f(x))/(△x)=\frac{-642.4-6.36}{4.2+0.7_{}} \\ (△f(x))/(△x)=\frac{-648.76}{4.9_{}} \\ (△f(x))/(△x)=-132.40 \end{gathered}`

The average rate of change = -132.40