Difference quotient question

Question

Find
f(a), f(a + h),
and the difference quotient

f(a + h) − f(a)

----------------
         h
,
where
h ≠ 0.

 

f(x) = x2 + 3

 

 

Find

f(a)=

f(a+h)=

f(a + h) − f(a)       =
----------------        
         h

 

Can not figure out how this problem is preformed.

Answer 1

f(x) = x² + 3

 

f(a) = a² + 3

 

f(a + h) = (a + h)² + 3

f(a + h) = a² + 2ah + h² + 3

 

f(a + h) - f(a) = a² + 2ah + h² + 3 - (a² + 3)

f(a + h) - f(a) = a² + 2ah + h² + 3 - a² - 3

f(a + h) - f(a) = a² + 2ah + h² 

 

[f(a + h) - f(a)] / h = (a² + 2ah + h²)/ h