Functions Math Question?

Question

Can some one help me solve thiS:

f(x) = x squared - 1; f(x+h) - f (x) divided by h


please ppl~~

Answer 1

you're basically solving for the derivative of this question using the proof of a derivative.

f(x) = x^2-1
f(x+h) ----> for every 'x', plug in 'x+h' = (x+h)^2-1 = x^2+2xh+h^2

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

= h(2x+h)/h = 2x+h.

The proof of the derivative states to evaluate the limit as h->0

Therefore, 2x+h where h = 0, simplifies to 2x

To verify, use the power rule to calculate f'(x), which is = 2x

Answer 2

f(x + h) = (x + h)^2 - 1
f(x + h) = ((x + h)(x + h)) - 1
f(x + h) = (x^2 + xh + xh + h^2) - 1
f(x + h) = x^2 + 2xh + h^2 - 1

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

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

(f(x + h) - f(x))/h = 2x + h

Answer 3

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