Question

Find and simplify each of the following for ​f(x)=5x^2−5x+8.

A: f(x+h)
B: f(x+h) - f(x)
C: (f(x+h) - f(x))/h

Thank you!

Answer 1

well if we let h --->0 we get the derivative :),
it better come out that way
​f(x)=5x^2−5x+8
f'(x) = 10 x - 5 (save for the end)
so
f(x+h) = 5(x+h)^2 - 5(x+h) + 8
= 5 x^2 + 10 x h +5 h^2 - 5 x - 5 h + 8
subtract f(x)
f(x+h) - f(x) =10 x h + 5 h^2 -5 h
divide by h
10 x + 5 h - 5
now to check against that derivative let h -->0
10 x - 5
:) sure enough