Answered

IDNLearn.com: Where your questions are met with thoughtful and precise answers. Ask your questions and receive reliable and comprehensive answers from our dedicated community of professionals.

Consider the function given by f(x)= x² +3. Find its average rate of change from x = -2 to x = 4.
Carefully show the work that leads to your final answer.

Sagot :

MrRoyalidn

Answer:

[tex]Rate = 2[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2 + 3[/tex]

Required

Determine the average rate of change from -2 to 4

This is calculated using:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

In this case:

[tex]a = -2[/tex]

[tex]b = 4[/tex]

So, we have:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{4 - (-2)}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{4 +2}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{6}[/tex]

Calculate f(4):

[tex]f(x) = x^2 + 3[/tex]

[tex]f(4) = 4^2 + 3[/tex]

[tex]f(4) = 19[/tex]

Calculate f(-2)

[tex]f(x) = x^2 + 3[/tex]

[tex]f(-2) = (-2)^2 + 3[/tex]

[tex]f(-2) = 7[/tex]

So:

[tex]Rate = \frac{f(4) - f(-2)}{6}[/tex]

[tex]Rate = \frac{19-7}{6}[/tex]

[tex]Rate = \frac{12}{6}[/tex]

[tex]Rate = 2[/tex]

The average rate of change is 2.

We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.