2.1 Average Rate of Change.

Question

let f be the function defined by f(x)= e^2x. the average rate if change of f over the interval [1,b] is 20 where b>1. which if the following is an equation that can be used to find the value of b

Answer 1

(e^2b - e^2)/(b-1) = 20 solve for b= about 1.289

Answer 2

Average rate of change is akin to the slope formula (y₂ - y₁)/(x₂ - x₁) and, for the interval [1,b] would be written as [f(b) - f(1)]/(b - 1). For f(x) = e^(2x) that makes the equation: [e^(2b) - e^2]/(b - 1) = 20.

Since you didn't list the equations noted in the problem, it's impossible to know if this is the form of the equation that they have listed.