For the function f ( x ) = 6x^2 + 5x − 9 evaluate and fully simplify each of the following.

Question

For the function f(x)=6x^2 + 5x − 9,evaluate and fully simplify each of the following.

f (x+h) = 

f (x+h) - f(x)/h =

Answer 1

f(x+h) = 6(x+h)²+5(x+h)-9 = 6x²+12xh+6h²+5x+5h-9

(f(x+h) - f(x))/h = (6x²+12xh+6h²+5x+5h-9 - 6x²-5x+9)/h

= (12xh+6h²+5h)/h = 12x+6h+5