Answered

Get comprehensive answers to your questions with the help of IDNLearn.com's community. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.

The function f ( x ) = 2 x ^2 − x − 4 models the shape of a ditch. What is the average slope over the interval −4 ≤ x ≤ 2?

Sagot :

MrRoyalidn

Answer:

[tex]Rate = -5[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x^2 - x - 4[/tex]

[tex]-4 \le x \le 2[/tex]

Required

Determine the average slope over the given interval

This is calculated as:

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

Where:

[tex]a = -4[/tex]

[tex]b =2[/tex]

So:

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

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

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

Solving for f(2) and f(-4), we have:

[tex]f(x) = 2x^2 - x - 4[/tex]

[tex]f(2) = 2 *2^2 -2 - 4[/tex]

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

[tex]f(-4) = 2*(-4)^2 - (-4) - 4[/tex]

[tex]f(-4) = 2*16 +4 - 4[/tex]

[tex]f(-4) = 32[/tex]

So, the equation becomes

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

[tex]Rate= \frac{2 - 32}{6}[/tex]

[tex]Rate= \frac{-30}{6}[/tex]

[tex]Rate = -5[/tex]

Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.