Answer:
[tex]\frac{f(x+h)-f(x)}{h}[/tex][tex]=2x - h[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 8 - x^2[/tex]
Required
Determine: [tex]\frac{f(x+h)-f(x)}{h}[/tex]
First, we calculate f(x + h)
[tex]f(x) = 8 - x^2[/tex]
[tex]f(x+h) = 8 - (x+h)^2[/tex]
[tex]f(x+h) =8- x^2-2xh-h^2[/tex]
So, we have:
[tex]\frac{f(x+h)-f(x)}{h}[/tex] [tex]= \frac{8- x^2-2xh-h^2 - 8 + x^2}{h}[/tex]
[tex]\frac{f(x+h)-f(x)}{h}[/tex] [tex]= \frac{8 - 8 + x^2- x^2-2xh-h^2}{h}[/tex]
[tex]\frac{f(x+h)-f(x)}{h}[/tex] [tex]= \frac{-2xh-h^2}{h}[/tex]
[tex]\frac{f(x+h)-f(x)}{h}[/tex][tex]=2x - h[/tex]
