Given the function g(x)=x^2-9x+16g(x)=x
2
−9x+16, determine the average rate of change of the function over the interval 1\le x \le 61≤x≤6.
help?

Question

Given the function g(x)=x^2-9x+16g(x)=x
​2
​​ −9x+16, determine the average rate of change of the function over the interval 1\le x \le 61≤x≤6.
 help?

Nathan Axel · Accepted Answer

#-2# #"the average rate of change is a measure of the slope of"# #"the "color(blue)"secant line ""over a closed interval"[a,b]# #"average rate of change is measured as"# #•color(white)(x)(f(b)-f(a))/(b-a)# #"here the closed interval is "[a,b]=[1,6]# #f(b)=f(6)=6^2-9(6)+16=36-54+16=#-2 #f(a)=f(1)=1-9+16=8# #rArr(-2-8)/(6-1)=(-10)/5=-2#

Jameson Allen · Answer

undefined To determine the average rate of change of the function $ g(x) = x^2 - 9x + 16 $ over the interval $ 1 \leq x \leq 6 $, you can use the formula for average rate of change, which is the difference in the function values divided by the difference in the corresponding x-values.

Average rate of change $ = \frac{{g(6) - g(1)}}{{6 - 1}} $

Evaluate $ g(6) $ and $ g(1) $:

$ g(6) = (6)^2 - 9(6) + 16 = 36 - 54 + 16 = -2 $

$ g(1) = (1)^2 - 9(1) + 16 = 1 - 9 + 16 = 8 $

Now, substitute these values into the formula:

Average rate of change $ = \frac{{-2 - 8}}{{6 - 1}} $

Average rate of change $ = \frac{{-10}}{{5}} $

Average rate of change $ = -2 $

So, the average rate of change of the function over the interval $ 1 \leq x \leq 6 $ is $ -2 $.

Given the function g(x)=x^2-9x+16g(x)=x ​2 ​​ −9x+16, determine the average rate of change of the function over the interval 1\le x \le 61≤x≤6. help?

Given the function g(x)=x^2-9x+16g(x)=x 2 −9x+16, determine the average rate of change of the function over the interval 1\le x \le 61≤x≤6. help?