Difference Quotient

[cheddacheese]

Question: Find and simplify the difference quotient of f,
[ f(x+h)-f(x)] / h; h does not = 0

the function that is given is
f(x)=-8x^4 -3x^2+1

I'm not sure If I got the right answer but this is what I got.
=(2xh+h^2-5h-2) / h

if this is right, this is the answer, because it can not be simplified, right?

THanks for any help!

 

[galactus]

If it is correct, you should get the derivative of \(\displaystyle -8x^{4}-3x^{2}+1\)

Which is \(\displaystyle -32x^{3}-6x\)

\(\displaystyle \lim_{h\to 0}\frac{(-8(x+h)^{4}-3(x+h)^{2}+1)-(-8x^{4}-3x^{2}+1)}{h}\)

\(\displaystyle \lim_{h\to 0}\frac{-32hx^{3}-48h^{2}x^{2}-32h^{3}x-6xh-8h^{4}-3h^{2}}{h}\)

If you expand out and cancel appropriately, you should get the derivative of said function.

 

[cheddacheese]

Opps. i put in the wrong function that was given. It should be
f(x)=x^2+5x-2

 

[galactus]

In that event, you're close.

Should be \(\displaystyle \lim_{x\to 0}\frac{2xh+h^{2}+5h}{h}\)

Do you get \(\displaystyle 2x+5\) as h approaches 0?.

 

[cheddacheese]

I'm sorry, I'm confused. Where did the -2 in the original equation go?

 

[galactus]

Where did it go?. The derivative of a constant is 0.

 

[Deleted member 4993]

If you want to find your mistake - please show your work (step by step).