SOLUTION: Given that f(x)= x^3-x+1, find (f(h)-f(-h))/2h Thanks!!

Question 824097: Given that f(x)= x^3-x+1, find (f(h)-f(-h))/2h
Thanks!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
f(x)= x^3-x+1

f(h)= h^3-h+1 ... replace EVERY copy of x with h

-------------------------------------------------------

f(x)= x^3-x+1

f(-h)= (-h)^3-(-h)+1 ... replace EVERY copy of x with -h

f(-h)= -h^3-(-h)+1

f(-h)= -h^3+h+1

-------------------------------------------------------

f(h)-f(-h) = (h^3-h+1) - (-h^3+h+1)

f(h)-f(-h) = h^3-h+1 + h^3 - h - 1

f(h)-f(-h) = 2h^3-2h

-------------------------------------------------------

So...

(f(h)-f(-h))/2h

turns into

(2h^3-2h)/2h

then you factor out 2h in the numerator to get

(2h(h^2-1))/2h

and then cancel out the '2h' terms to get

h^2 - 1

and then you can optionally factor to get

(h-1)(h+1)

=======================================================

So the answer is either h^2 - 1 or (h-1)(h+1)

They are equivalent. The second expression is the factored form of the first (using the difference of squares rule).
RELATED QUESTIONS
Given f(x)=(x^3)+1, find... (answered by jim_thompson5910)

If f(x) = x(x+2), find (f(x+h)-f(x-h))/2h (answered by MathLover1)

If F(x) = 2x, find [(F(x+h) -... (answered by Nate)

Find(f-h)(x).Given f(x)=x+1 and... (answered by Fombitz)

Given f(x)=x+1 and h(x)=2x-3, find... (answered by josgarithmetic)

Find(f-h)(x). Given f(x)=x+1 and... (answered by Fombitz)

Given f(x)=x+1 and h(x)=2x-3, find... (answered by josgarithmetic)

Given f(x)=x+1 and h(x)= 2x-3, find... (answered by addingup,MathTherapy)

find f(x+h)/h-f(x)/h when... (answered by Fombitz)