Given f(x) = 17-xwhat is the average rate of change in f(x) over the interval [1, 5]?

Answer:The average rate of change in f(x) over the interval [1, 5] is -1Step-by-step explanation:Hi! Let me help you to understand this problem. Here we have the following function:[tex]f(x) = 17-x[/tex]We need to compute the Average Rate of Change (ARC) in [tex]f(x)[/tex] over the interval [tex][1, 5][/tex]. So what is the average rate of change of a function? In general, for a nonlinear graph whose slope changes at each point, the average rate of change between any two points [tex](x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})[/tex] is defined as the slope of that line through that two points. Here we have a linear function, so the average rate of change will be the slope of the line:So:[tex]ARC=m=-1[/tex]This can also be calculated as:[tex]ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} \\ \\ ARC=\frac{17-5-(17-1)}{5-1} \\ \\ ARC=-1[/tex]