Suppose the function f is defined by

f(x) = – 1* x^2 – 4* x + 2.
In the text box below, enter the Average Rate of Change of f as x goes from 1 to 3. Your answer should be a number; do not enter letters or other symbols in the text box. Your answer must be exact, please do not round off your answer. For example, do not round off 1/3 to be .33. After entering your answer, click the Save Answer button.

-8

Step-by-step explanation:

GIven a function , the rate of change of the function over an interval is given by

where

is the value of the function calculated in

is the value of the function calculated in

In this problem, the function is

The interval is

So we have:

Therefore, the rate of change of the function is

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).