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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

 Oct 11, 2018
 #1
avatar+99585 
+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 ]

 

cool cool cool

 Oct 11, 2018
edited by CPhill  Oct 11, 2018
 #2
avatar+10254 
+1

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

laugh

 Oct 11, 2018

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