Question

Find the average rate of change for the function over the given interval. y equals e Superscript x between xequalsnegative 2 and xequals1

Answer 1

(e³ - 1)/3e²

Explanation:

Given the function y = e^x between the interval x = -2 and x =1, the average rate of change for the function will be the slope of the function expressed as m = Δy/Δx where;

Δy = f(b)-f(a) and Δx = b-a

m = f(b)-f(a)/b-a where a and b is the interval [-2, 1]

m = f(1)-f(-2)/1-(-2)

m = f(1)-f(-2)/3

Given the function f(x) = e^x,

at the end point x = b, f(1) = e^1; f(1) = e

at the end point x = a, f(-2) = e^-2; f(-2) = 1/e²

m = (e - 1/e²)/3

m = [(e³ - 1)/e²]/3

m = (e³ - 1)/e² * 1/3

m = (e³ - 1)/3e²

Hence, the average rate of change for the function at the interval [-2, 1] is (e³ - 1)/3e²