I don't understand how to do ARoC

Question

let f(x)=7x^2 ... Find a value A such that the average rate of change of f(x) from 1 to A equals 70

Answer 1

[f(A) - f(1)] / A = 70

f(A) - f(1) = 70A

7A² - 7 = 70A

 

Can you solve for A and answer?

Answer 2

[f(A) - f(1)] / [A - 1] = 70

 

7A² - 7 = 70A - 70

 

7A² - 70A + 63 = 0

 

A² - 10A + 9 = 0

 

(A - 9)(A - 1) = 0

 

A = 9 or A = 1

 

Since A can't be 1, A = 9.