Get detailed and reliable answers to your questions on IDNLearn.com. Ask your questions and receive prompt, detailed answers from our experienced and knowledgeable community members.

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

Sagot :

Answer:

The average rate of change = -132.40

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:

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

The average rate of change = -132.40