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

Question

myininaya · Answer

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

whpalmer4 · Answer

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 $$8x-1$$

anonymous · Answer

says that is wrong

myininaya · Answer

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

anonymous · Answer

im sorry, it says h cannot equal zero

whpalmer4 · Answer

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).