Question

Find and simplify the difference quotient f(x+h)-f(x)/h,for the function f(x)=4x^2-x-1

Answer 1

\[\frac{(4(x+h)^2-(x+h)-1)-(4x^2-x-1)}{h}\]
now multiply
combine like terms

Answer 2

Same drill.

\[(4*(x+h)^2-(x+h) - 1 - (4x^2-x-1))/h\]
\[=(4*(x^2+2xh+h^2)-(x+h)-1-4x^2+x+1)/h\]
\[=(4x^2+8xh+4h^2-x-h-1-4x^2+x+1)/h\]
\[=(8xh+4h^2-h)/h = (8x+4h-1)/h\]

As h->0, that will go to \[8x-1\]

Answer 3

says that is wrong

Answer 4

your question didn't ask for the limit as h->0

Answer 5

im sorry, it says h cannot equal zero

Answer 6

Sorry, made a mess of the final simplification:

\[=(8xh+4h^2-h)/h=8x+4h-1\]

(and the limit which wasn't asked for is still 8x-1).