Calculus Question

Question

(Please show all of your work when answering the question. It helps me out quite a bit. Thank you in advance. -Student)

Consider the function f(x)= -4x^2+1x+1

a) For the given function f, the expression f(x+h)-f(x)/h can be simplified to the form Ax+Bh+C, where A, B, and C are constants.

Answer: f(x+h)-f(x)/h =?

Answer 1

f(x) = -4x^2 +x+1

f(x+h) = -4(x+h)^2 + (x+h) + 1

=- 4x^2 - 8xh - 4h^2 + x+h+1

f(x+h)-f(x) = -8xh -4h^2 +h

divide by h

= -8x -8h +1

=Ax+Bh +C with A=-8, B=-8, C=1