Help with precalc homework please

Let f(x) = -2x^2 +x -5

b) Find [ f(x+h)-f(x)] / h, h is not equal to 0

can someone please help me understand how to go about solving this problem. id really appreciate it. thanks!

[-2(x^2+2xh+h^2) + (x+h) - 5 + 2x^2 - x + 5]/h
=[-4xh - 2h^2 + h]/h
=[-4x -2h + 1]
Now let h->0 and get 1-4x

Angel -

This is called a "difference quotient". Check your book for some extra examples.

Here is how to solve your problem ...

Plug in (x + h) into the equation like this:

-2(x+h)^2 +(x+h) -5, then subtract (-2x^2 +x -5) and divide the whole mess by h

{[-2(x+h)^2 +(x+h) -5] - (-2x^2 +x -5)} / h

After you do all the math and cancel out the h's, you will get this answer:

-4x + 1

Hope that helped

f(x+h) = -2(x+h)^2 +(x+h) -5 =

[ f(x+h)-f(x)] = -2x^2 -4xh -h^2 +x+h-5 +2x^2 -x +5

= -4xh -h^2 +h


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

(note - when you then take the limit as h--> 0, you have the derivative of f(x) )