Question

Let f(x)=8x^2. Find a value A such that the average rate of change of f(x) from 1 to A equals 96. A=

Answer 1

Giiven function f(x) = 8x^2

a = 1, b = A

f(1) = 8(1)^2

= 8

f(A) = 8A^2

Average rate ofchange = (f(b)-f(a))/(b-a)

96 = [8A^2-8]/[A-1]

96(A-1) = 8A^2-8

96A-96 = 8A^2-8

Bring all terms to one side.

8A^2-96A-8+96 = 0

8A^2-96A+88 = 0

Divide to each side by 8.

A^2-12A+11 = 0

Now factorise it.

A^2-11A-A+11 = 0

A(A-11)-1(A-11) = 0

(A-11)(A-1) = 0

A-11 = 0 and A-1 = 0

A = 11 and A = 1

⇒A = 11