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User Mher
by
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1 Answer

5 votes

Answer:


(f(x+h)-f(x))/(h)
=2x + h

Explanation:

Given


f(x)= x^2 + 2

Required

Determine:
(f(x+h)-f(x))/(h)

First, we calculate f(x + h)


f(x)= x^2 + 2


f(x+h) = (x+h)^2+2


f(x+h) = x^2+2xh+h^2+2

So, we have:


(f(x+h)-f(x))/(h)
= (x^2 + 2xh + h^2 + 2 - x^2 - 2)/(h)


(f(x+h)-f(x))/(h)
= (x^2 - x^2+ 2xh + h^2 + 2 - 2)/(h)


(f(x+h)-f(x))/(h)
= (2xh + h^2)/(h)


(f(x+h)-f(x))/(h)
=2x + h

User Ondrej Bozek
by
3.6k points