Question

f(x) = x^2 + 6
Find using the difference quotient
f(a + h) − f(a)/h

Answer 1

This will help you get started.... f(a+h) means you need to plug in a+h in place of x....\[\Large f(a+h) = (x+h)^2 +6\]^ now foil/simplify that.

same thing for f(a)\[\Large f(a) = a^2 + 6\]

Then you want to plug those into (f(a + h) − f(a))/h

Answer 2

First find f(a+ h). To find this you need to substitute (a + h) in for x
f(a+h) = ( a+h) ^2 + 6
f(a+h) = (a+h)(a+h) +6
f(a + h )= a^2 + 2ah + h^2 + 6
Now find f(a)
f(a) = x^2 +6
f(a) = a^2 + 6
Now substitute all of this in ! Literally do a cut and paste ! Where you have f(a+h),
paste in a^2 +2ah +h^2 +6
Now, you must also paste in what you found for f(a) ! When you paste this in, you need to put it in parentheses preceded by a negative! We must do f(a+h) - f(a)
So, the numerator would look like a:
(a^2 +2ah +h^2+6) -(a^2+6)
This simplifies to a^2 +2ah +h^2 +6 -a^2 -6
2ah +h^2
Now, all of this must be put over h
Factor h out of the numerator
h(2a +h) / h
Cancel the h out and you are left with
2a+h

Answer 3

thank you!!

Answer 4

f(x) = 2/x + 5
FInd using difference quotient

Answer 5

f(a)=2/a+5
f(a+h)= 2/(a+h)+5

Answer 6

You should post it as a new question. But you'll just have to add the fractions in that one too.