Find and simplify (*f*(a+h) - *f*(a))/h for *f*(x)= 3x^2 -5

I got this on a test and it seemed like there wasn't enough information to solve and wondered if anyone else could

Tahu8100
Oct 11, 2018

#1**+1 **

We have

f (a+ h) = 3(a + h)^2 - 5 = 3 [ a^2 + 2ah + h^2 ] - 5 =

3a^2 + 6ah + 3h^2 - 5

f(a) = 3(a)^2 - 5 = 3a^2 - 5

So

[ f(a + h) - f(a) ] / h =

[ (3a^2 + 6ah + 3h^2 - 5) - (3a^2 - 5) ] / h =

[6ah + 3h^2] / h =

h [ 6a + 3h ] / h =

6a + 3h

Note that if we let h approach 0, we get 6a = the derivative of 3x^2 - 5 when x = a ]

CPhill
Oct 11, 2018