Given the function g(x) = 6^x, section a is from x = 1 to x = 2 and section b is from x = 3 to x = 4. part a: find the average rate of change in each section. part b: how many times greater is the average rate of change of section b than section a?

Part a: the average rate of change over a certain interval is the slope of the line that connects the left and right points  on a graph. i have included a picture from my notes of this concept.so for you question, the average rate of change over a section iswhere  are the x-coordinates of the boundaries  of the section/interval.for section a,  . (the order doesn't matter; we could have also done . as long as we have the boundaries of the section.) and the value of  at those x-coordinates can be calculated: so the average rate of change for section a  isfor section b,  . and the value of  at those x-coordinates can be calculated: so the average rate of change for section b ispart b: the average rate of change of section b is 30 times greater than section a. if you multiply the average rate of change of section a by 30, you'll get section b's avg rate of change.