Let 𝑓(𝑥) be the function 9x2−3x+4 . Then the quotient f(4+h)−f(4)h can be simplified to ah+b for a= ? b= ?

Answer 1

f(x) = 9x^2 -3x + 4

f(x+h) = 9(x+h)^2 -3(x+h) +4 = 9x^2+18xh+9h^2 -3x-3h +4

f(x+h)-f(x) = 18xh-3h +9h^2

(f(x+h)-f(x))/h = 18x-3+9h

ah+b? then a=9 and b = 18x-3

unless you're finding the limit as h goes to zero, then

the quotient = 18x-3

and maybe your ah+b was intended to really be ax+b with a=18 and b=-3