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