Answer:
[tex]\dfrac{f(4+h)-f(4)}{h}=8h-20[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]f(x) = 8x^2-84x+6[/tex]
We have to evaluate:
[tex]\dfrac{f(4+h)-f(4)}{(4+h)-4}=\dfrac{f(4+h)-f(4)}{h}[/tex]
[tex]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[/tex]
[tex]f(4) = 8(4)^2-84(4)+6 = -202[/tex]
Putting values, we get
[tex]\dfrac{f(4+h)-f(4)}{h}\\\\=\dfrac{8h^2-20h-202+202}{h}\\\\=\dfrac{8h^2-20h}{h}\\\\=8h-20[/tex]
