Question

For f (x) = 8x superscript 2 end of superscript, - 84x + 6, find and simplify fraction whose numerator is f (4 + h) - f (4) and whose denominator is h end of fraction, .

Answer 1

`(f(4+h)-f(4))/(h)=8h-20`

Explanation:

We are given the following in the question:

`f(x) = 8x^2-84x+6`

We have to evaluate:

`(f(4+h)-f(4))/((4+h)-4)=(f(4+h)-f(4))/(h)`

`f(4+h) = 8(4+h)^2-84(4+h)+6\\= 8(16+h^2+8h)-84(4+h)+6\\=128+8h^2+64h-336-84h+6\\=8h^2-20h-202`

`f(4) = 8(4)^2-84(4)+6 = -202`

Putting values, we get

`(f(4+h)-f(4))/(h)\\\\=(8h^2-20h-202+202)/(h)\\\\=(8h^2-20h)/(h)\\\\=8h-20`