Function: f(x)=2x+2
Part 1: f(x+h)=2(x+h)+2
Part 2: f(x)=2x+2
(2x+2h+2-(2x+2))/h
(2x+2h+2-2x-2)/h
2h/h
Solution: 2
Part 1: f(x+h)=2(x+h)+2
Part 2: f(x)=2x+2
(2x+2h+2-(2x+2))/h
(2x+2h+2-2x-2)/h
2h/h
Solution: 2
Function: f(x)=x²+3
f(x+h)=(x+h)²+3
=(x+h)(x+h)+3
=x²+hx+hx+h²+3
Part 1: f(x+h)=x²+2hx+h²+3
Part 2: f(x)=x²+3
(x²+h²+2hx+3-(x²+3))/h
(h²+2hx)/h
Solution:2x+h
f(x+h)=(x+h)²+3
=(x+h)(x+h)+3
=x²+hx+hx+h²+3
Part 1: f(x+h)=x²+2hx+h²+3
Part 2: f(x)=x²+3
(x²+h²+2hx+3-(x²+3))/h
(h²+2hx)/h
Solution:2x+h
Function: f(x)=2x³
f(x+h)=2(x+h)³
=2(x+h)(x+h)(x+h)
=2(x²+hx+hx+h²)(x+h)
=2(x³+hx²+hx²+xh²+hx²+xh²+xh²+h³)
=2(x³+3hx²+3xh²+h³)
Part 1: f(x+h)=2x³+6hx²+6xh²+2h³
Part 2:f(x)=2x³
(2x³+6hx²+6xh²+2h³-2x³)/h
Solution: 6x²+2h²+6xh
f(x+h)=2(x+h)³
=2(x+h)(x+h)(x+h)
=2(x²+hx+hx+h²)(x+h)
=2(x³+hx²+hx²+xh²+hx²+xh²+xh²+h³)
=2(x³+3hx²+3xh²+h³)
Part 1: f(x+h)=2x³+6hx²+6xh²+2h³
Part 2:f(x)=2x³
(2x³+6hx²+6xh²+2h³-2x³)/h
Solution: 6x²+2h²+6xh