Question

The concept and full method

Answer 1

Answer:

Step-by-step explanation:

This kinda looks like the limiting definition of a derivative.  

Anyway, what we are doing with the f(2 + h) is evaluating f(x) with 2+h in place for x.  That looks like this:

f(2 + h) = 2(2 + h) - 3 which simplifies to

f(2 + h) = 4 + 2h - 3 which simplifies to

2h + 1

From that we are subtracting f(2).  What we are doing with that is evaluating f(x) with 2 in place for x.  That looks like this:

f(2) = 2(2) - 3 which simplifies to

f(2) = 4 - 3 which simplifies to

f(2) = 1.  Now put those together over h to get:

$\frac{f(2+h)-f(2)}{h}=\frac{2h+1-1}{h}=\frac{2h}{h}=2$