SOLUTION: find f(a+h)-f(a)/h for f(x)=x^2+3x+1
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Question 311326: find f(a+h)-f(a)/h for f(x)=x^2+3x+1
Found 2 solutions by JBarnum, solver91311:
Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website!
ur dealing with 3 completely different variables where a,h,and x are all unknown so unless there is more to this question, then there is nothing to solve, if this is a question your teacher gave u....that teacher needs to put a bit more thought into the question.
my answer would be: need more information to solve
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ x^2\ +\ 3x\ +\ 1)
So, )
is
\ =\ a^2\ +\ 3a\ +\ 1)
and )
is
\ =\ (a\ +\ h)^2\ +\ 3(a\ +\ h)\ +\ 1)
so
\ -\ f(a)}{h}\ =\ \frac{\left((a\ +\ h)^2\ +\ 3(a\ +\ h)\ +\ 1\right)\ -\ \left(a^2\ +\ 3a\ +\ 1\right)}{h})
Expanding the binomials:
\ -\ f(a)}{h}\ =\ \frac{\left(a^2\ +\ 2ah\ +\ h^2\ +\ 3a\ +\ 3h\ +\ 1\right)\ -\ \left(a^2\ +\ 3a\ +\ 1\right)}{h})
Removing parentheses and collecting like terms:
\ -\ f(a)}{h}\ =\ \frac{2ah\ +\ h^2\ +\ 3h}{h})
Then eliminating the factor of 
common to both numerator and denominator:
\ -\ f(a)}{h}\ =\ 2a\ +\ h\ +\ 3)
And that's all there is to it.
John
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