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

Answer:

$\dfrac{f(4+h)-f(4)}{h}=8h-20$

Step-by-step explanation:

We are given the following in the question:

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

We have to evaluate:

$\dfrac{f(4+h)-f(4)}{(4+h)-4}=\dfrac{f(4+h)-f(4)}{h}$

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

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

Putting values, we get

$\dfrac{f(4+h)-f(4)}{h}\\\\=\dfrac{8h^2-20h-202+202}{h}\\\\=\dfrac{8h^2-20h}{h}\\\\=8h-20$