Question

Let f(x) be the function 11x2−9x+7. Then the quotient
f(6+h)−f(6)h can be simplified to ah+b for:
a=
and
b=

Answer 1

I have a sneaking suspicion that you mean

[f(6+h)−f(6)]/ h

f(6+h) = 11(6+h)^2 - 9(6+h) + 7
f(6) = 11(6)^2 - 9(6) + 7
---------------------------------
f(6+h) -f(h) = 11(12h+h^2) -9h
= 132 h+ 11 h^2 - 9h
= 123 h + 11 h^2
now divide by h
= 11 h + 123
a = 11
b = 123

check with calculus
f' = 22 x - 9
when x = 6
f' = 132 - 9 = 123 check