Question

Find average rate of change f(x)=-4x^(2)-3x-4 ; [-1,3]

Answer 1

The rate of change of the given function at [-1,3] is 5

Further explanation:

Given function is:

$f(x) = 4x^2-3x-4$

And the interval is:

[-1,3]

In order to find the rate of chnage of function the given function's value is calculated at both points and divided by their difference

The formula is:

$Rate\ of\ change= \frac{f(x_2)-f(x_1)}{x_2-x_1}$

Here,

x_1 = -1

x_2 = 3

So,

$f(-1) = 4(-1)^2-3(-1)-4\\=4(1) +3-4\\=4-1\\=3\\f(3) = 4(3)^2-3(3)-4\\= 4(9)-9-4\\=36-13\\=23$

Putting the values in the rate of change formula:

$Rate\ of\ change= \frac{23-3}{3-(-1)}\\= \frac{23-3}{3+1}\\=\frac{20}{4} \\=5$

The rate of change of the given function at [-1,3] is 5

Keywords: Rate of change, functions

Learn more about functions:

• brainly.com/question/3225044
• brainly.com/question/3568205

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